A vector has magnitude units

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A vector

\mathbf{b}

has magnitude

10

units. Its direction cosines with the

x

– and

y

–axes are

\cos\alpha=\dfrac{3}{5}

and

\cos\beta=-\dfrac{4}{5}

, respectively. (a) Determine

\cos\gamma

, the direction cosine of

\mathbf{b}

with the

z

–axis. (b) Hence obtain the components of

\mathbf{b}

along the three coordinate axes. (c) Verify by direct calculation that the magnitude found from the components in part (b) is indeed

10

units.