If , and is a linearly independent system of vectors, examine the system , and ,…

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

Problem

\mathbf{u}

\mathbf{v}

and

\mathbf{w}

is a linearly independent system of vectors, examine the system

\mathbf{p}

\mathbf{q}

and

\mathbf{r}

, where

\mathbf{p} = (\cos a)\mathbf{u} + (\cos b)\mathbf{v} + (\cos c)\mathbf{w}

\mathbf{q} = (\sin a)\mathbf{u} + (\sin b)\mathbf{v} + (\sin c)\mathbf{w}

\mathbf{r} = \sin(x+a)\mathbf{u} + \sin(x+b)\mathbf{v} + \sin(x+c)\mathbf{w}

for linearly dependent.