If , and are position vectors of the vertices , and of , show that the area of is .…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are position vectors of the vertices

A

B

and

C

\triangle ABC

, show that the area of

\triangle ABC

\frac{1}{2} |\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}|

. Deduce the condition for points

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

to be collinear.