The value of

Question:

$\frac{1}{2}[\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}]$ 16. If $\vec{a}, \vec{b}, \vec{c} \quad$ determine the vertices of a triangle, show that

gives the

vector area of the triangle. Hence deduce the condition that the three points $\vec{a}, \vec{b}, \vec{c}$ are collinear. Also find the unit vector normal to the plane of the triangle.

Solution: