Answer
$v\times w=-i-6j-k.$
$w\times v=i+4j+k.$
$w\times w=v\times v=0.$
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 $D=v\times w=i(1\cdot(-1)-3\cdot0)-j(3\cdot(-1)-3\cdot1)+k(3\cdot0-1\cdot1)=-i-6j-k.$
We know that $w\times v=-v\times w=-(-i-6j-k)=i+4j+k.$
We also know that $w\times w=v\times v=0.$
