Answer
$v\times w=i((-1)\cdot(-1)-2\cdot1)-j(2\cdot(-1)-2\cdot0)+k(2\cdot1-(-1)\cdot0)=-i+2j+2k.$
We know that $w\times v=-v\times w=-(-i+2j+2k)=i-2j-2k.$
We also know that $w\times w=v\times v=0.$
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 $D=v\times w=i((-1)\cdot(-1)-2\cdot1)-j(2\cdot(-1)-2\cdot0)+k(2\cdot1-(-1)\cdot0)=-i+2j+2k.$
We know that $w\times v=-v\times w=-(-i+2j+2k)=i-2j-2k.$
We also know that $w\times w=v\times v=0.$
