Show that the points ,

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

Problem

Show that the points

P(\mathbf{a} + 2\mathbf{b} + \mathbf{c})

Q(\mathbf{a} - \mathbf{b} - \mathbf{c})

R(3\mathbf{a} + \mathbf{b} + 2\mathbf{c})

and

S(5\mathbf{a} + 3\mathbf{b} + 5\mathbf{c})

are coplanar given that

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are non-coplanar.