Mathematics

Problem

Find the values of

m

and

n

so that

\mathbf{u}=\langle 1,\,m,\,3\rangle

and

\mathbf{v}=\langle n,\,2,\,-1\rangle

are perpendicular, and their sum

\mathbf{u}+\mathbf{v}

is perpendicular to

\mathbf{w}=\langle 2,\,-1,\,4\rangle