文档介绍：求证: u×(v×w )=( u·w)v -(u·v ) w 并问: u×(v×w ) 与(u×v)×w是否相等?u,v, w 为矢量。证明: ?????? kji kjiwv xyyxzxxzyzzy zyx zyxwvwvwvwvwvwv ???????????????????????????? k j i kjiwvu yzzyyzxxzx xyyxxyzzyzzxxzzxyyxy xyyxzxxzyzzy zy xwvwvuwvwvu wvwvuwvwvuwvwvuwvwvu wvwvwvwvwvwv uuu???????????????????????? kji vwu zyxzzyyxxvvvwuwuwu???????????? kji wvu zyxzzyyxx???????????????????????????????????? k j i kji kji wvuvwuyzzyyzxxzx xyyxxyzzyz zxxzzxyyxy zyxzzyyxx zyxzzyyxxwvwvuwvwvu wvwvuwvwvu wvwvuwvwvu wu??????????????????????????????? wvuvwuwvu????????????? kji kjivu xyyxzxxzyzzy zyx zyxvuvuvuvuvuvu vvv uuu???????????????????????????? k j i kjiwvu zxxzxyzzyy yzzyzxyyxxxyyxyzxxzz zyx xyyxzxxzyzzyvuvuwvuvuw vuvuwvuvuwvuvuwvuvuw ?????????????????????? wvuwvu?????? 求证: (A×B)×(C×D )=B(A·C×D)-A(B·C×D)=C(A·B×D)-D(A·B×C) 证明: ?????? kji kjiBA xyyxzxxzyzzy zyx zyxBABABABABABA BBB AAA?????????????? kji kjiDC xyyxzxxzyzzy zyx zyxDCDCDCDCDCDC C?????????????? kji kjiCB xyyxzxxzyzzy zyx C BBB?????????????? kji kjiDB xyyxzxxzyzzy zyx zyxDBDBDBDBDBDB DDD BBB???????????? xyyxzxxzyzzy xyyxzxxzyzzyDCDCDCDCDCDC BABABABABABA?????????? kjiDCBA?????? xyyxzzxxzyyzzyx DCDCADCDCADCDCA????????DCA?????? xyyxzzxxzyyzzyx DCDCBDCDCBDCDCB????????DCB?????????????????????????????????????????????????????????????????? k j i kji kji DCBADCABzxxzyyzzyxz zxxzyyzzyxz xyyxzyzzyxy xyyxzyzzyxy xyyxzzxxzyx xyyxzzxxzyx zyx xyyxzzxxzyyzzyx zyx xyyxzzxxzyyzzyxDCDCBDCDCBA DCDCADCDCAB DCDCBDCDCBA DCDCADCDCAB DCDCBDCDCBA DCDCADCDCAB AAA DCDCBDCDCBDCDCB BBB DCDCADCDCADCDCA????????????????????????????????????????????????????? xyyxzzxxzyyzzyx DCDBADBDBADBDBA????????DBA?????? xyyxzzxxzyyzzyxCBCBACBCBACBCBA????????CBA?????????????????????????????????????????????????????????????????? k j i kji kji CBADDBACyxxyzxyyxzz yxxyzxyyxzz xzzxyzxxzyy xzzxyzxxzyy zyyzxyzzyxx zyyzxyzzyxx zyx xyyxzzxxzyyzzyx zyx xyyxzzxxzyyzzyxCACABCBCBAD DADABDBDBAC CACABCBCBAD DADABDBDBAC CACABCBCBAD DADABDBDBAC DDD C DBDBADBDBADBDBA?????????????????????????