Question

Given A= i+2j+3k and B= 2i+j-k, find AxB

Answer 1

$$A\times B=\begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 2 & 1 & -1 \end{vmatrix}$$

$$=i\begin{vmatrix} 2 & 3 \\ 1 & -1 \end{vmatrix}-j\begin{vmatrix} 1 & 3 \\ 2 & -1 \end{vmatrix}+k\begin{vmatrix} 1 & 2 \\ 2 & 1 \end{vmatrix}$$

$$=i(-2-3)-j(-1-6)+k(1-4)$$

$$=-5i+7j-3k$$

$A\times B=-5i+7j-3k$