Question

Find the vector, not with determinants, but by using properties of cross products. k × (i − 3j)

Answer 1

$\mathbf k\times(\mathbf i-3\mathbf j)=(\mathbf k\times\mathbf i)-3(\mathbf k\times\mathbf j)$
$=\mathbf j-3(-\mathbf i)$
$=3\mathbf i+\mathbf j$