Mathematics

Problem

For the vector

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

and

\mathbf{q}=\langle 3,\,-1,\,4\rangle

: a. (i) Find the value of

k

for which

\mathbf{p}

is perpendicular to

\mathbf{q}

. b. (ii) Using this value of

k

, calculate

|\mathbf{p}|