Question

Use a determinant to find the area of the
triangle with the given vertices (0, 0), (3, 6),
(6, −2)

Answer 1

Let
$$
A=3\hat i+6\hat j\\
B=6\hat i-2\hat j
$$
Find \(|A\times B|\) (i.e. the determinant of the cross product):
$$
det\begin{bmatrix}
\hat{i}& \hat{j} & \hat{k}\\
3& 6& 0\\
6& -2 &0
\end{bmatrix}\\
=|\hat i(0)-\hat j(0)+\hat k(-6-36)|\\
=|-42\hat k|\\
=42
$$

Answer 2

would I divide it by 2
?

Answer 3

yes, you are correct!