Computing $U \times V$

Question

Problem:

Given $$ U = (2,1,3) $$ $$ U = (4,-2,2) $$ find $U \times V$.

Answer:

\begin{align*} U \times V &= \begin{vmatrix} i & j & k \\ 2 & 1 & 3 \\ 4 & -2 & 2 \end{vmatrix} = i \begin{vmatrix} 1 & 3 \\ -2 & 2 \\ \end{vmatrix} - j \begin{vmatrix} 2 & 3 \\ 4 & 2 \end{vmatrix} + k \begin{vmatrix} 2 & 1 \\ 4 & -2 \end{vmatrix} \\ U \times V &= i(2 + 6) - j(4-12) + k(-4-4) \\ U \times V &= 8i + 8j - 8k \end{align*}

However, the books answer is: $$ (5,8,-6) $$ Where did I go wrong?

Answer 1

The answer given is correct subject to a typo. That is, the second vectori is $V$ not $U$.