If and are non-coplanar vectors

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

Problem

\boldsymbol{a}, \boldsymbol{b}

and

\boldsymbol{c}

are non-coplanar vectors, then prove that the four points

2 \boldsymbol{a} + 3 \boldsymbol{b} - \boldsymbol{c}, \boldsymbol{a} - 2 \boldsymbol{b} + 3 \boldsymbol{c}, 3 \boldsymbol{a} + 4 \boldsymbol{b} - 2 \boldsymbol{c}

and

\boldsymbol{a} - 6 \boldsymbol{b} + 6 \boldsymbol{c}

are coplanar.