Mathematics

Problem

Determine the real numbers

p

and

q

such that the vectors

\mathbf{a}=\langle p,\,3,\,-1\rangle

and

\mathbf{b}=\langle 2,\,q,\,4\rangle

satisfy both

\mathbf{a}\cdot\mathbf{b}=0

and

|\mathbf{a}|=5