Two non-zero vectors and satisfy the following conditions: • and the direction…

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

Problem

Two non-zero vectors

\mathbf{a}

and

\mathbf{b}

satisfy the following conditions: •

|\mathbf{a}|=10

and the direction cosines of

\mathbf{a}

are in the ratio

2: -3: 6

. •

|\mathbf{b}|=15

and

\mathbf{b}

is parallel to

3\hat{i}-4\hat{j}+12\hat{k}

. (i) Determine the exact Cartesian form of

\mathbf{a}

and of

\mathbf{b}

. (ii) Show that the vector

\mathbf{c}=\mathbf{a}+\mathbf{b}

makes an obtuse angle with the

y

-axis. (iii) Find a unit vector perpendicular to

\mathbf{c}

and lying in the

xz

-plane.