Simplify and express the result solely in terms of , , ,

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

Problem

Simplify

(2\mathbf{a}-3\mathbf{b}+\mathbf{c})\cdot(\mathbf{a}+4\mathbf{b}-2\mathbf{c})

and express the result solely in terms of

\mathbf{a}\cdot\mathbf{a}

\mathbf{b}\cdot\mathbf{b}

\mathbf{c}\cdot\mathbf{c}

\mathbf{a}\cdot\mathbf{b}

\mathbf{b}\cdot\mathbf{c}

and

\mathbf{c}\cdot\mathbf{a}