Mathematics

Problem

Consider the vectors

\mathbf{a}=\langle k,1,2\rangle

and

\mathbf{b}=\langle 3,k,-1\rangle

. a. (i) Find the value(s) of

k

for which the angle between

\mathbf{a}

and

\mathbf{b}

90^\circ

. b. (ii) For the value of

k

obtained in (i), determine the angle (to the nearest degree) between

\mathbf{a}+\mathbf{b}

and

\mathbf{a}-\mathbf{b}