Vectors and are non-collinear

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

Problem

Vectors

\boldsymbol{a}

and

\boldsymbol{b}

are non-collinear. Find for what values of

x

vectors

\boldsymbol{c} = (x - 2)\boldsymbol{a} + \boldsymbol{b}

and

\boldsymbol{d} = (2x + 1)\boldsymbol{a} - \boldsymbol{b}

are collinear?