Answer
$43$
Work Step by Step
We have $\vec{AB}= \lt 1,-4 \gt -\lt -6,0 \gt =\lt 7, -4 \gt$
and $\vec{AC}=\lt 3,1 \gt -\lt -6,0 \gt =\lt 9,1 \gt$
$\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\7&-4&0\\9&1&0\end{vmatrix}=0-0+(7+36)\hat{k}= 43\hat{k}$.
Therefore, $|\vec{AB}\times\vec{AC}|=\sqrt {(43)^2}=43$
