Question

Даны точки A(5;2;-1),B(1;-1;0),C(3;-1;0).Найти координаты векторного произведения

[BC-2CA,CB].

Answer 1

Ответ: {0; -4; -12}

$A(5;2;-1) quad B(1;-1;0) quad C(3;-1;0)\\overline {BC} = {3 - 1; -1 - (-1); 0-0 } = {2;0; 0 }\\overline {CA} = {5-3;2-(-1); -1 - 0 } = {2;3;-1 }\ \ overline a = overline {BC} - 2cdot overline{CA} = {2-2cdot 2; 0-2cdot 3; 0 - 2cdot(-1)} = {-2; -6; 2} \ \ overline b =overline {CB} = -overline {BC} = {-2; 0; 0 }$

Найдём векторное произведение

$overline a times overline b = left|begin{array}{ccc}overline i &overline j&overline k\-2&-6&2\-2&0&0end{array}right| = overline i left|begin{array}{rc} -6 & 2 \ 0 & 0end{array}right| - overline j left|begin{array}{rc} -2 & 2 \ -2 & 0 end{array}right|+overline k left|begin{array}{rc} -2 & -6 \ -2 & 0end{array}right| = \ \ \ = 0,overline i -4overline j - 12overline k = {0;-4; -12}$