Question

Determine the cross product of x times y when x= 4i-5j+3k and y= -2i+3j-k

Answer 1

$\mathbf x\times\mathbf y=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\4&-5&3\\-2&3&-1\end{vmatrix}$
$\mathbf x\times\mathbf y=\begin{vmatrix}-5&3\\3&-1\end{vmatrix}\mathbf i-\begin{vmatrix}4&3\\-2&-1\end{vmatrix}\mathbf j+\begin{vmatrix}4&-5\\-2&3\end{vmatrix}\mathbf k$
$\mathbf x\times\mathbf y=-4\,\mathbf i-2\,\mathbf j+2\,\mathbf k$