diff --git a/main.py b/main.py
index 7622630..4e86335 100644
--- a/main.py
+++ b/main.py
@@ -7,4 +7,147 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
 @Email   : snowykami@outlook.com
 @File    : main.py
 @Software: PyCharm
-"""
\ No newline at end of file
+"""
+import logging
+
+from mbcp.mp_math.line import Line3
+from mbcp.mp_math.plane import Plane3
+from mbcp.mp_math.point import Point3
+
+# def ac8s4e4():
+#     """
+#     第八章第四节例4
+#     问题：求与两平面x-4z-3=0和2x-y-5z-1=0的交线平行且过点(-3, 2, 5)的直线方程。
+#     """
+#     correct_ans = Line3(4, 3, 1, 1)
+#
+#     pl1 = Plane3(1, 0, -4, -3)
+#     pl2 = Plane3(2, -1, -5, -1)
+#     p = Point3(-3, 2, 5)
+#     """解法1"""
+#     # 求直线方向向量s
+#     s = pl1.normal @ pl2.normal
+#     actual_ans = Line3.from_point_and_direction(p, s)
+#
+#     logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+#     assert actual_ans == correct_ans
+#
+#     """解法2"""
+#     # 过点p且与pl1平行的平面pl3
+#     pl3 = pl1.cal_parallel_plane3(p)
+#     # 过点p且与pl2平行的平面pl4
+#     pl4 = pl2.cal_parallel_plane3(p)
+#     # 求pl3和pl4的交线
+#     actual_ans = pl3.cal_intersection_line3(pl4)
+#     print(pl3, pl4, actual_ans)
+#
+#     logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+#     assert actual_ans == correct_ans
+#
+#
+# ac8s4e4()
+import logging
+
+from mbcp.mp_math.mp_math_typing import RealNumber
+from mbcp.mp_math.utils import Approx
+
+
+def three_var_func(x: RealNumber, y: RealNumber) -> RealNumber:
+    return x ** 3 * y ** 2 - 3 * x * y ** 3 - x * y + 1
+
+
+class TestPartialDerivative:
+    # 样例来源：同济大学《高等数学》第八版下册 第九章第二节 例6
+    def test_2v_1o_1v(self):
+        """测试二元函数关于第一个变量(x)的一阶偏导 df/dx"""
+
+        from mbcp.mp_math.utils import Approx
+        from mbcp.mp_math.equation import get_partial_derivative_func
+
+        partial_derivative_func = get_partial_derivative_func(three_var_func, 0)
+
+        # assert partial_derivative_func(1, 2, 3) == 4.0
+        def df_dx(x, y):
+            """原函数关于x的偏导"""
+            return 3 * (x ** 2) * (y ** 2) - 3 * (y ** 3) - y
+
+        logging.info(f"Expected: {df_dx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
+        assert Approx(partial_derivative_func(1, 2)) == df_dx(1, 2)
+
+    def test_2v_1o_2v(self):
+        """测试二元函数关于第二个变量(y)的一阶偏导 df/dy"""
+
+        from mbcp.mp_math.utils import Approx
+        from mbcp.mp_math.equation import get_partial_derivative_func
+
+        partial_derivative_func = get_partial_derivative_func(three_var_func, 1)
+
+        def df_dy(x, y):
+            """原函数关于y的偏导"""
+            return 2 * (x ** 3) * y - 9 * x * (y ** 2) - x
+
+        logging.info(f"Expected: {df_dy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
+        assert Approx(partial_derivative_func(1, 2)) == df_dy(1, 2)
+
+    def test_2v_2o_12v(self):
+        """高阶偏导d^2f/(dxdy)"""
+
+        from mbcp.mp_math.utils import Approx
+        from mbcp.mp_math.equation import get_partial_derivative_func
+
+        partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 1))
+
+        def df_dxdy(x, y):
+            """原函数关于y和x的偏导"""
+            return 6 * x ** 2 * y - 9 * y ** 2 - 1
+
+        logging.info(f"Expected: {df_dxdy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
+        assert Approx(partial_derivative_func(1, 2)) == df_dxdy(1, 2)
+
+    def test_2v_2o_1v2(self):
+        """二阶偏导d^2f/(dx^2)"""
+
+        from mbcp.mp_math.utils import Approx
+        from mbcp.mp_math.equation import get_partial_derivative_func
+
+        partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0))
+
+        def df_dydx(x, y):
+            """原函数关于x和y的偏导"""
+            return 6 * x * y ** 2
+
+        logging.info(f"Expected: {df_dydx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
+        assert Approx(partial_derivative_func(1, 2)) == df_dydx(1, 2)
+
+    def test_2v_3o_1v3(self):
+        """高阶偏导d^3f/(dx^3)"""
+
+        from mbcp.mp_math.utils import Approx
+        from mbcp.mp_math.equation import get_partial_derivative_func
+
+        partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0, 0))
+
+        def d3f_dx3(x, y):
+            """原函数关于x的三阶偏导"""
+            return 6 * (y ** 2)
+
+        logging.info(f"Expected: {d3f_dx3(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
+        assert Approx(partial_derivative_func(1, 2)) == d3f_dx3(1, 2)
+
+    def test_possible_error(self):
+        from mbcp.mp_math.equation import get_partial_derivative_func
+        def two_vars_func(x: RealNumber, y: RealNumber) -> RealNumber:
+            return x ** 2 * y ** 2
+
+        partial_func = get_partial_derivative_func(two_vars_func, 0)
+        partial_func_2 = get_partial_derivative_func(two_vars_func, (0, 0))
+        assert Approx(partial_func_2(1, 2)) == 8
+
+
+TestPartialDerivative().test_2v_1o_1v()
+TestPartialDerivative().test_2v_1o_2v()
+TestPartialDerivative().test_2v_2o_12v()
+TestPartialDerivative().test_2v_2o_1v2()
+TestPartialDerivative().test_2v_3o_1v3()
+
+TestPartialDerivative().test_possible_error()
diff --git a/mbcp/mp_math/angle.py b/mbcp/mp_math/angle.py
new file mode 100644
index 0000000..5dc140f
--- /dev/null
+++ b/mbcp/mp_math/angle.py
@@ -0,0 +1,94 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/26 上午6:29
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : angle.py
+@Software: PyCharm
+"""
+from typing import overload
+
+from .const import PI
+
+
+class AnyAngle:
+    def __init__(self, value: float, is_radian: bool = False):
+        """
+        任意角度。
+        Args:
+            value: 角度或弧度值
+            is_radian: 是否为弧度，默认为否
+        """
+        if is_radian:
+            self.radian = value
+        else:
+            self.radian = value * PI / 180
+
+    @property
+    def complementary(self) -> "AnyAngle":
+        """
+        余角：两角的和为90°。
+        Returns:
+            余角
+        """
+        return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
+
+    @property
+    def supplementary(self) -> "AnyAngle":
+        """
+        补角：两角的和为180°。
+        Returns:
+            补角
+        """
+        return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
+
+    @property
+    def degree(self) -> float:
+        """
+        角度。
+        Returns:
+            弧度
+        """
+        return self.radian * 180 / PI
+
+    @property
+    def minimum_positive(self) -> "AnyAngle":
+        """
+        最小正角。
+        Returns:
+            最小正角度
+        """
+        return AnyAngle(self.radian % (2 * PI))
+
+    @property
+    def maximum_negative(self) -> "AnyAngle":
+        """
+        最大负角。
+        Returns:
+            最大负角度
+        """
+        return AnyAngle(-self.radian % (2 * PI), is_radian=True)
+
+    def __add__(self, other: "AnyAngle") -> "AnyAngle":
+        return AnyAngle(self.radian + other.radian, is_radian=True)
+
+    def __sub__(self, other: "AnyAngle") -> "AnyAngle":
+        return AnyAngle(self.radian - other.radian, is_radian=True)
+
+    def __mul__(self, other: float) -> "AnyAngle":
+        return AnyAngle(self.radian * other, is_radian=True)
+
+    @overload
+    def __truediv__(self, other: float) -> "AnyAngle":
+        ...
+
+    @overload
+    def __truediv__(self, other: "AnyAngle") -> float:
+        ...
+
+    def __truediv__(self, other):
+        if isinstance(other, AnyAngle):
+            return self.radian / other.radian
+        return AnyAngle(self.radian / other, is_radian=True)
diff --git a/mbcp/mp_math/equation.py b/mbcp/mp_math/equation.py
index efecc63..9352af0 100644
--- a/mbcp/mp_math/equation.py
+++ b/mbcp/mp_math/equation.py
@@ -46,13 +46,15 @@ class CurveEquation:
 
 def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc:
     """
-    求N元函数一阶偏导函数。
+    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     Args:
         func: 函数
         var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
         epsilon: 偏移量
     Returns:
         偏导函数
+    Raises:
+        ValueError: 无效变量类型
     """
     if isinstance(var, int):
         def partial_derivative_func(*args: Var) -> Var:
diff --git a/mbcp/mp_math/line.py b/mbcp/mp_math/line.py
index 8bcc38a..07f9537 100644
--- a/mbcp/mp_math/line.py
+++ b/mbcp/mp_math/line.py
@@ -5,49 +5,67 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
 @Time    : 2024/8/6 下午12:57
 @Author  : snowykami
 @Email   : snowykami@outlook.com
-@File    : line.py
+@File    : other.py
 @Software: PyCharm
 """
-from typing import TYPE_CHECKING
+import math
+from typing import TYPE_CHECKING, overload
+from .vector import Vector3
 
 if TYPE_CHECKING:
-    from .point import Point3   # type: ignore
+    from .angle import AnyAngle
+    from .plane import Plane3
+    from .point import Point3
 
 
 class Line3:
     def __init__(self, a: float, b: float, c: float, d: float):
         """
         三维空间中的直线。
-        :param a:
-        :param b:
-        :param c:
-        :param d:
+        Args:
+            a: 直线方程的系数a
+            b: 直线方程的系数b
+            c: 直线方程的系数c
+            d: 直线方程的常数项d
         """
         self.a = a
         self.b = b
         self.c = c
         self.d = d
 
-    def __str__(self):
-        return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
+    def cal_angle(self, other: "Line3") -> "AnyAngle":
+        """
+        计算直线和直线或面之间的夹角。
+        Args:
+            other: 另一条直线或面
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+        if isinstance(other, Line3):
+            return self.direction.cal_angle(other.direction)
+        elif isinstance(other, Plane3):
+            return self.direction.cal_angle(other.normal).complementary  # 方向向量和法向量的夹角的余角
+        else:
+            raise TypeError(f"Unsupported type: {type(other)}")
 
-    def get_perpendicular(self, point: "Point3") -> "Line3":
+    @property
+    def direction(self) -> "Vector3":
         """
-        获取直线经过指定点p的垂线。
-        :param point: 指定点p，直线外的点
-        :return: 垂直于self且过点p的直线
+        直线的方向向量。
+        Returns:
+            方向向量
         """
-        a = -self.b
-        b = self.a
-        c = 0
-        d = -(a * point.x + b * point.y + self.c * point.z)
-        return Line3(a, b, c, d)
+        return Vector3(self.a, self.b, self.c)
 
-    def get_intersection(self, line: "Line3") -> "Point3":
+    def cal_intersection(self, line: "Line3") -> "Point3":
         """
-        获取两条直线的交点。
-        :param line:
-        :return:
+        计算两条直线的交点。
+        Args:
+            line: 另一条直线
+        Returns:
+            交点
         """
 
         if self.is_parallel(line):
@@ -70,21 +88,39 @@ class Line3:
 
         return Point3(x, y, z)
 
+    def cal_perpendicular(self, point: "Point3") -> "Line3":
+        """
+        计算直线经过指定点p的垂线。
+        Args:
+            point: 指定点
+        Returns:
+            垂线
+        """
+        a = -self.b
+        b = self.a
+        c = 0
+        d = -(a * point.x + b * point.y + self.c * point.z)
+        return Line3(a, b, c, d)
+
     def is_parallel(self, line: "Line3") -> bool:
         """
         判断两条直线是否平行。
         直线平行的条件是它们的法向量成比例
-        :param line:
-        :return:
+        Args:
+            line: 另一条直线
+        Returns:
+            是否平行
         """
-        return self.a * line.b == self.b * line.a and self.c * line.b == self.d * line.a
+        return self.direction.is_parallel(line.direction)
 
     def is_collinear(self, line: "Line3") -> bool:
         """
         判断两条直线是否共线。
         直线共线的条件是它们的法向量成比例且常数项也成比例
-        :param line:
-        :return:
+        Args:
+            line: 另一条直线
+        Returns:
+            是否共线
         """
         return self.is_parallel(line) and (self.d * line.b - self.b * line.d) / (self.a * line.b - self.b * line.a) == 0
 
@@ -92,10 +128,56 @@ class Line3:
         """
         判断两条直线是否共面。
         两条直线共面的条件是它们的方向向量和法向量的叉乘为零向量
-        :param line:
-        :return:
+        Args:
+            line: 另一条直线
+        Returns:
+            是否共面
         """
         direction1 = (-self.c, 0, self.a)
         direction2 = (line.c, -line.b, 0)
         cross_product = direction1[0] * direction2[1] - direction1[1] * direction2[0]
         return cross_product == 0
+
+    @classmethod
+    def from_point_and_direction(cls, point: "Point3", direction: "Vector3") -> "Line3":
+        """
+        工厂函数 由点和方向向量构造直线(点向式构造)。
+        Args:
+            point: 点
+            direction: 方向向量
+        Returns:
+            直线
+        """
+        a, b, c = direction.x, direction.y, direction.z
+        d = -(a * point.x + b * point.y + c * point.z)
+        return cls(a, b, c, d)
+
+    @classmethod
+    def from_two_points(cls, p1: "Point3", p2: "Point3") -> "Line3":
+        """
+        工厂函数 由两点构造直线。
+        Args:
+            p1: 点1
+            p2: 点2
+        Returns:
+            直线
+        """
+        direction = p2 - p1
+        return cls.from_point_and_direction(p1, direction)
+
+    def __eq__(self, other) -> bool:
+        """
+        判断两条直线是否等价。
+        Args:
+            other:
+
+        Returns:
+
+        """
+        return self.a / other.a == self.b / other.b == self.c / other.c == self.d / other.d
+
+    def __repr__(self):
+        return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
+
+    def __str__(self):
+        return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
diff --git a/mbcp/mp_math/plane.py b/mbcp/mp_math/plane.py
index d8fc4e6..5041303 100644
--- a/mbcp/mp_math/plane.py
+++ b/mbcp/mp_math/plane.py
@@ -1,10 +1,124 @@
 # -*- coding: utf-8 -*-
 """
-Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+平面模块
+"""
+import math
+from typing import TYPE_CHECKING
 
-@Time    : 2024/8/6 下午1:45
-@Author  : snowykami
-@Email   : snowykami@outlook.com
-@File    : plane.py
-@Software: PyCharm
-"""
\ No newline at end of file
+import numpy as np
+
+from .vector import Vector3
+from .line import Line3
+from .point import Point3
+
+if TYPE_CHECKING:
+    from .angle import AnyAngle
+
+
+class Plane3:
+    def __init__(self, a: float, b: float, c: float, d: float):
+        """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a:
+            b:
+            c:
+            d:
+        """
+        self.a = a
+        self.b = b
+        self.c = c
+        self.d = d
+
+    def cal_angle(self, other: "Line3 | Plane3") -> "AnyAngle":
+        """
+        计算平面与平面之间的夹角。
+        Args:
+            other: 另一个平面
+        Returns:
+            夹角弧度
+        Raises:
+            TypeError: 不支持的类型
+        """
+        if isinstance(other, Line3):
+            return self.normal.cal_angle(other.direction).complementary
+        elif isinstance(other, Plane3):
+            return AnyAngle(math.acos(self.normal * other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+        else:
+            raise TypeError(f"Unsupported type: {type(other)}")
+
+    def cal_distance(self, other: "Plane3 | Point3") -> float:
+        """
+        计算平面与平面或点之间的距离。
+        Args:
+            other: 另一个平面或点
+        Returns:
+            距离
+        Raises:
+            TypeError: 不支持的类型
+        """
+        if isinstance(other, Plane3):
+            return 0
+        elif isinstance(other, Point3):
+            return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+        else:
+            raise TypeError(f"Unsupported type: {type(other)}")
+
+    def cal_intersection_line3(self, other: "Plane3") -> "Line3":
+        """
+        计算两平面的交线。该方法有问题，待修复。
+        Args:
+            other: 另一个平面
+        Returns:
+            交线
+        """
+        # 计算两法向量的叉积作为交线的方向向量
+        s = self.normal.cross(other.normal)  # 交线的方向向量
+        # 联立两平面方程求交线的一点
+        # 两平面方程联立得到的方程组
+        # | a1x + b1y + c1z = -d1
+        # | a2x + b2y + c2z = -d2
+        # 用numpy解方程组
+        a = np.array([[self.a, self.b, self.c], [other.a, other.b, other.c]])
+        b = np.array([-self.d, -other.d])
+        p = np.linalg.lstsq(a, b, rcond=None)[0]
+        return Line3.from_point_and_direction(Point3(*p), s)
+
+    def cal_parallel_plane3(self, point: "Point3") -> "Plane3":
+        """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point: 指定点
+        Returns:
+            平面
+        """
+        return Plane3.from_point_and_normal(point, self.normal)
+
+    @property
+    def normal(self) -> "Vector3":
+        """
+        平面的法向量。
+        Returns:
+            法向量
+        """
+        return Vector3(self.a, self.b, self.c)
+
+    @classmethod
+    def from_point_and_normal(cls, point: "Point3", normal: "Vector3") -> "Plane3":
+        """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point: 平面上的一点
+            normal: 法向量
+        Returns:
+            平面
+        """
+        a, b, c = normal.x, normal.y, normal.z
+        d = -a * point.x - b * point.y - c * point.z  # d = -ax - by - cz
+        return cls(a, b, c, d)
+
+    def __repr__(self):
+        return f"Plane3({self.a}, {self.b}, {self.c}, {self.d})"
+
+    def __str__(self):
+        return f"{self.a}x + {self.b}y + {self.c}z + {self.d} = 0"
diff --git a/mbcp/mp_math/point.py b/mbcp/mp_math/point.py
index bfd5ed6..4583994 100644
--- a/mbcp/mp_math/point.py
+++ b/mbcp/mp_math/point.py
@@ -44,6 +44,7 @@ class Point3:
         :param other:
         :return:
         """
+        from .vector import Vector3
         return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
 
     def __truediv__(self, other: float) -> "Point3":
diff --git a/mbcp/mp_math/py.typed b/mbcp/mp_math/py.typed
index a8a7f97..e69de29 100644
--- a/mbcp/mp_math/py.typed
+++ b/mbcp/mp_math/py.typed
@@ -1,2 +0,0 @@
-# py.typed
-partial
\ No newline at end of file
diff --git a/mbcp/mp_math/vector.py b/mbcp/mp_math/vector.py
index fa987fd..ed2c3c3 100644
--- a/mbcp/mp_math/vector.py
+++ b/mbcp/mp_math/vector.py
@@ -1,9 +1,10 @@
+import math
 from typing import overload, TYPE_CHECKING
 
-import numpy as np
+from .point import Point3
 
 if TYPE_CHECKING:
-    from .point import Point3  # type: ignore
+    from .angle import AnyAngle
 
 
 class Vector3:
@@ -14,75 +15,59 @@ class Vector3:
         :param y:
         :param z:
         """
-        self._x = x
-        self._y = y
-        self._z = z
-        self._length = (x ** 2 + y ** 2 + z ** 2) ** 0.5
-        self._normalized = self / self._length
+        self.x = x
+        self.y = y
+        self.z = z
 
-    def __str__(self):
-        return f"Vector3({self._x}, {self._y}, {self._z})"
+    def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+        """
+        计算两个向量之间的夹角。
+        Args:
+            other: 另一个向量
+        Returns:
+            夹角
+        """
+        return AnyAngle(math.acos(self * other / (self.length * other.length)), is_radian=True)
 
-    def _unset_properties(self):
-        self._length = None
-        self._normalized = None
+    def is_parallel(self, other: 'Vector3') -> bool:
+        """
+        判断两个向量是否平行。
+        Args:
+            other: 另一个向量
+        Returns:
+            是否平行
+        """
+        return self @ other == Vector3(0, 0, 0)
 
-    @property
-    def x(self):
-        return self._x
-
-    @x.setter
-    def x(self, value):
-        self._x = value
-        self._unset_properties()
-
-    @property
-    def y(self):
-        return self._y
-
-    @y.setter
-    def y(self, value):
-        self._y = value
-        self._unset_properties()
-
-    @property
-    def z(self):
-        return self._z
-
-    @z.setter
-    def z(self, value):
-        self._z = value
-        self._unset_properties()
+    def cross(self, other: 'Vector3') -> 'Vector3':
+        """
+        向量积 叉乘：V1 @ V2 -> V3
+        Args:
+            other:
+        Returns:
+            叉乘结果，为0向量则两向量平行，否则垂直于两向量
+        """
+        return Vector3(self.y * other.z - self.z * other.y,
+                       self.z * other.x - self.x * other.z,
+                       self.x * other.y - self.y * other.x)
 
     @property
     def length(self) -> float:
         """
         向量的模。
-        :return:
+        Returns:
+            模
         """
-        if self._length is None:
-            self._length = (self._x ** 2 + self._y ** 2 + self._z ** 2) ** 0.5
-        return self._length
+        return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
 
     @property
-    def normalized(self) -> 'Vector3':
+    def unit(self) -> 'Vector3':
         """
-        返回该向量的单位向量。
-        :return:
+        获取该向量的单位向量。
+        Returns:
+            单位向量
         """
-        if self._normalized is None:
-            self._normalized = self / self.length
-        return self._normalized
-
-    def normalize(self):
-        """
-        自体归一化。
-        """
-        self._x /= self.length
-        self._y /= self.length
-        self._z /= self.length
-        self._length = 1
-        self._normalized = self
+        return self / self.length
 
     @overload
     def __add__(self, other: 'Vector3') -> 'Vector3':
@@ -96,16 +81,28 @@ class Vector3:
         """
         V + P -> P\n
         V + V -> V
-        :param other:
-        :return:
+        Args:
+            other:
+        Returns:
+
         """
         if isinstance(other, Vector3):
-            return Vector3(self._x + other.x, self._y + other.y, self._z + other.z)
+            return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
         elif isinstance(other, Point3):
-            return Point3(self._x + other.x, self._y + other.y, self._z + other.z)
+            return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
         else:
             raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
 
+    def __eq__(self, other):
+        """
+        判断两个向量是否相等。
+        Args:
+            other:
+        Returns:
+            是否相等
+        """
+        return self.x == other.x and self.y == other.y and self.z == other.z
+
     def __radd__(self, other: 'Point3') -> 'Point3':
         """
         P + V -> P\n
@@ -113,7 +110,7 @@ class Vector3:
         :param other:
         :return:
         """
-        return Point3(self._x + other.x, self._y + other.y, self._z + other.z)
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
 
     @overload
     def __sub__(self, other: 'Vector3') -> 'Vector3':
@@ -127,25 +124,28 @@ class Vector3:
         """
         V - P -> P\n
         V - V -> V
-        :param other:
-        :return:
+        Args:
+            other:
+        Returns:
         """
         if isinstance(other, Vector3):
-            return Vector3(self._x - other.x, self._y - other.y, self._z - other.z)
+            return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
         elif isinstance(other, Point3):
-            return Point3(self._x - other.x, self._y - other.y, self._z - other.z)
+            return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
         else:
             raise TypeError(f"unsupported operand type(s) for -: 'Vector3' and '{type(other)}'")
 
     def __rsub__(self, other: Point3):
         """
         P - V -> P
-        :param other:
-        :return:
+        Args:
+            other:
+        Returns:
+
         """
 
         if isinstance(other, Point3):
-            return Point3(other.x - self._x, other.y - self._y, other.z - self._z)
+            return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
         else:
             raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
 
@@ -159,34 +159,52 @@ class Vector3:
 
     def __mul__(self, other):
         """
-        乘法。包括点乘和数乘。
-        :param other:
-        :return:
+        点乘法。包括点乘和数乘。
+        V * V -> float\n
+        Args:
+            other:
+        Returns:
+            float
+        Raises:
+            TypeError: 不支持的类型
         """
         if isinstance(other, (int, float)):
-            return Vector3(self._x * other, self._y * other, self._z * other)
+            return Vector3(self.x * other, self.y * other, self.z * other)
         elif isinstance(other, Vector3):
-            return self._x * other.x + self._y * other.y + self._z * other.z
+            return self.x * other.x + self.y * other.y + self.z * other.z
         else:
             raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
 
     def __rmul__(self, other: float) -> 'Vector3':
         """
         右乘。
-        :param other:
-        :return:
+        Args:
+            other:
+        Returns:
+            乘积
         """
-        return Vector3(self._x * other, self._y * other, self._z * other)
+        return Vector3(self.x * other, self.y * other, self.z * other)
 
     def __matmul__(self, other: 'Vector3') -> 'Vector3':
         """
-        叉乘。
-        :param other: 另一个向量
-        :return: 叉乘结果向量
+        向量积 叉乘：V1 @ V2 -> V3
+        Args:
+            other:
+        Returns:
+            叉乘结果，为0向量则两向量平行，否则垂直于两向量
         """
-        return Vector3(self._y * other.z - self._z * other.y,
-                       self._z * other.x - self._x * other.z,
-                       self._x * other.y - self._y * other.x)
+        return Vector3(self.y * other.z - self.z * other.y,
+                       self.z * other.x - self.x * other.z,
+                       self.x * other.y - self.y * other.x)
 
     def __truediv__(self, other: float) -> 'Vector3':
-        return Vector3(self._x / other, self._y / other, self._z / other)
+        return Vector3(self.x / other, self.y / other, self.z / other)
+
+    def __neg__(self):
+        return Vector3(-self.x, -self.y, -self.z)
+
+    def __repr__(self):
+        return f"Vector3({self.x}, {self.y}, {self.z})"
+
+    def __str__(self):
+        return f"Vector3({self.x}, {self.y}, {self.z})"
diff --git a/mbcp/py.typed b/mbcp/py.typed
index a8a7f97..e69de29 100644
--- a/mbcp/py.typed
+++ b/mbcp/py.typed
@@ -1,2 +0,0 @@
-# py.typed
-partial
\ No newline at end of file
diff --git a/tests/test_line3.py b/tests/test_line3.py
new file mode 100644
index 0000000..9ea3c3c
--- /dev/null
+++ b/tests/test_line3.py
@@ -0,0 +1,33 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/26 上午7:54
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : test_line3.py
+@Software: PyCharm
+"""
+import logging
+
+from mbcp.mp_math.point import Point3
+from mbcp.mp_math.vector import Vector3
+from mbcp.mp_math.line import Line3
+
+
+class TestLine3:
+
+    def test_point_and_normal_factory(self):
+        """
+        测试通过点和法向量构造直线
+        """
+        correct_ans = Line3(1, -2, 3, -8)
+
+        p = Point3(2, -3, 0)
+        n = Vector3(1, -2, 3)
+
+        actual_ans = Line3.from_point_and_direction(p, n)
+        logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+        assert actual_ans == correct_ans
+
+
diff --git a/tests/test_plane3.py b/tests/test_plane3.py
new file mode 100644
index 0000000..2729177
--- /dev/null
+++ b/tests/test_plane3.py
@@ -0,0 +1,29 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/26 上午9:07
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : test_plane3.py
+@Software: PyCharm
+"""
+import logging
+
+from mbcp.mp_math.line import Line3
+from mbcp.mp_math.plane import Plane3
+
+
+class TestPlane3:
+
+    def test_intersection_line3(self):
+        """
+        测试平面的交线
+        """
+        correct_ans = Line3(4, 3, 1, 1)
+
+        pl1 = Plane3(1, 0, -4, 23)
+        pl2 = Plane3(2, -1, -5, 33)
+        actual_ans = pl1.cal_intersection_line3(pl2)
+        logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+        assert actual_ans == correct_ans
diff --git a/tests/test_vector.py b/tests/test_vector.py
deleted file mode 100644
index f2bcc97..0000000
--- a/tests/test_vector.py
+++ /dev/null
@@ -1,22 +0,0 @@
-# -*- coding: utf-8 -*-
-"""
-Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
-
-@Time    : 2024/8/6 下午1:05
-@Author  : snowykami
-@Email   : snowykami@outlook.com
-@File    : test_vector.py
-@Software: PyCharm
-"""
-from mbcp.mp_math.vector import Vector3
-from mbcp.mp_math.point import Point3
-
-
-def test_v():
-    v1 = Vector3(1, 2, 3)
-    v2 = Vector3(4, 5, 6)
-    v3 = v1 + v2
-    assert v3._x == 5
-    assert v3._y == 7
-    assert v3._z == 9
-    print("test_v 1111passed")
diff --git a/tests/test_vector3.py b/tests/test_vector3.py
new file mode 100644
index 0000000..e7f737e
--- /dev/null
+++ b/tests/test_vector3.py
@@ -0,0 +1,52 @@
+# -*- coding: utf-8 -*-
+"""
+Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved 
+
+@Time    : 2024/8/26 上午6:58
+@Author  : snowykami
+@Email   : snowykami@outlook.com
+@File    : test_question_1.py
+@Software: PyCharm
+"""
+import logging
+
+from mbcp.mp_math.vector import Vector3
+
+
+class TestVector3:
+
+    """测试问题集"""
+    def test_vector_cross_product(self):
+        """
+        测试向量叉乘
+        Returns:
+        """
+        v1 = Vector3(1, 2, 3)
+        v2 = Vector3(3, 4, 5)
+        actual_ans = v1 @ v2
+        correct_ans = Vector3(-2, 4, -2)
+        logging.info(f"正确答案{correct_ans}    实际答案{v1 @ v2}")
+
+        assert correct_ans == actual_ans
+
+    def test_determine_vector_parallel(self):
+        """
+        测试判断向量是否平行
+        Returns:
+        """
+        v1 = Vector3(1, 2, 3)
+        v2 = Vector3(3, 6, 9)
+        actual_ans = v1.is_parallel(v2)
+        correct_ans = True
+        logging.info("v1和v2是否平行：%s", v1.is_parallel(v2))
+        assert correct_ans == actual_ans
+
+        v1 = Vector3(1, 2, 3)
+        v2 = Vector3(3, 6, 8)
+        actual_ans = v1.is_parallel(v2)
+        correct_ans = False
+        logging.info("v1和v2是否平行：%s", v1.is_parallel(v2))
+        assert correct_ans == actual_ans
+
+
+
diff --git a/tests/test_word_problem.py b/tests/test_word_problem.py
new file mode 100644
index 0000000..72f09b5
--- /dev/null
+++ b/tests/test_word_problem.py
@@ -0,0 +1,43 @@
+# -*- coding: utf-8 -*-
+"""
+应用题测试集
+"""
+import logging
+
+from mbcp.mp_math.line import Line3
+from mbcp.mp_math.plane import Plane3
+from mbcp.mp_math.point import Point3
+
+
+class TestWordProblem:
+
+    def test_c8s4e4(self):
+        """
+        同济大学《高等数学》第八版 下册 第八章第四节例4
+        问题：求与两平面x-4z-3=0和2x-y-5z-1=0的交线平行且过点(-3, 2, 5)的直线方程。
+        """
+        correct_ans = Line3(4, 3, 1, 1)
+
+        pl1 = Plane3(1, 0, -4, -3)
+        pl2 = Plane3(2, -1, -5, -1)
+        p = Point3(-3, 2, 5)
+        """解法1"""
+        # 求直线方向向量s
+        s = pl1.normal @ pl2.normal
+        actual_ans = Line3.from_point_and_direction(p, s)
+
+        logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+        assert actual_ans == correct_ans
+
+        """解法2"""
+        # 过点p且与pl1平行的平面pl3
+        pl3 = pl1.cal_parallel_plane3(p)
+        # 过点p且与pl2平行的平面pl4
+        pl4 = pl2.cal_parallel_plane3(p)
+        # 求pl3和pl4的交线
+        actual_ans = pl3.cal_intersection_line3(pl4)
+        print(pl3, pl4, actual_ans)
+
+        logging.info(f"正确答案：{correct_ans}    实际答案：{actual_ans}")
+        assert actual_ans == correct_ans
+