If , and are non-coplanar vectors, prove that , and are…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are non-coplanar vectors, prove that

3\mathbf{a} - 7\mathbf{b} - 4\mathbf{c}

3\mathbf{a} - 2\mathbf{b} + \mathbf{c}

and

\mathbf{a} + \mathbf{b} + 2\mathbf{c}

are coplanar.