Mathematics

Problem

A non-zero vector

\mathbf{a}

is parallel to the line of intersection of the plane determined by the vectors,

\hat{i}, \hat{i} + \hat{j}

and the plane determined by the vectors

\hat{i} - \hat{j}

and

\hat{i} + \hat{k}

. Find the angle between

\mathbf{a}

and

\hat{i} - 2\hat{j} + 2\hat{k}