Answer
$v\times w=-8+5j+14k.$
$w\times v=8i-5j-14k.$
$w\times w=v\times v=0.$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
We know that if we have two vectors $v=ai+bj+ck$ and $w=di+ej+fk$, then $v\times w$ can be obtained by the determinant of: \[
\left[\begin{array}{rrr}
i & j & k \\
a &b & c \\
d &e & f \\
\end{array} \right]
\]
Hence here $D=v\times w=i((-4)\cdot1-2\cdot2)-j(1\cdot1-2\cdot3)+k(1\cdot2-(-4)\cdot3)=-8+5j+14k.$
We know that $w\times v=-v\times w=-(-8+5j+14k)=8i-5j-14k.$
We also know that $w\times w=v\times v=0.$
