Answer
$v \times w=i +5j -7k$
$w \times v =-i-5j+7k$
and $ v \times v = w \times w =0$
Work Step by Step
Let us consider the two vectors $v=xi+yj+zk$ and $w=pi+qj+rk$; then the cross product of the two vectors $v$ and $w$ can be computed in the form of the determinant as:
$ v \times w=\begin{vmatrix}
i & j & k \\
x & y & z \\
p & q & r \\ \end{vmatrix}$
We have:
$det =v \times w =[(3)(-1)-(2)(-2)] i -j [(-1)(-1) - (2)(3)]+k [(-1)(-2) -(3) (3)]=i +5j -7k$
Recall that $v \times w= -w \times v=-i-5j+7k$
and $ v \times v = w \times w =0$
