Answer to Question #121879 in Analytic Geometry for Samson

Question

Given

α=i+2j+3k,

β=2i+j−k find

α×β

Answer 1

Solution.

$α=i+2j+3k;$

$β=2i+j−k$;

$α×β=\begin{vmatrix} i & j&k \\ 1& 2&3\\ 2&1&-1 \end{vmatrix}=i(2\sdot(-1)-1\sdot3)-j(1\sdot(-1)-2\sdot3)+$

$+k(1\sdot1-2\sdot2)=i(-5)-j(-7)+k(-3)=-5i+7j-3k;$

Answer: $α×β=-5i+7j-3k.$