mbcp/assets/zht_api_mp_math_vector.md.CEPTxRVM.lean.js

2 lines
12 KiB
JavaScript
Raw Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",19),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t("",1),Q=[k],m=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},""),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t("",7),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t("",1),F=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,""),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,""),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,""),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t("",1),V=[H],w=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t("",26),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t("",1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t("",1),W=[K],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t("",119);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式,"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default};