Mathematics

Problem

Let

\mathbf{p}=3\mathbf{i}+2\mathbf{j}-\mathbf{k}

and

\mathbf{q}=\mathbf{i}-4\mathbf{j}+2\mathbf{k}

. (a) Find a vector that is perpendicular to both

\mathbf{p}

and

\mathbf{q}

and whose

z

–component is positive. (b) Reduce the vector obtained in part (a) to a unit vector.