Answer
$$ v\times w=
-i+2j-5k.
$$
Work Step by Step
$$ v\times w=
\left|\begin{array}{rrr}{i} & {j} & {k} \\ {1} & {2} & {1} \\ {3} & {1} & {1}\end{array}\right|=i \left|\begin{array}{rrr} {2} & {1} \\ {1} & {1}\end{array}\right|-j\left|\begin{array}{rrr} {1} & {1} \\ {3} & {1}\end{array}\right|+k\left|\begin{array}{rrr}{1} & {2} \\ {3} & {1}\end{array}\right|\\
=i(2-1)-j(1-3)+k(1-6)\\
=-i+2j-5k.
$$
