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