Show that points with position vectors

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

Problem

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

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

and

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

are collinear. It is given that vectors

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are non-coplanar.