Mathematics

Problem

Let

\mathbf{A}

be vector parallel to line of intersection of planes

P_1

and

P_2

. Plane

P_1

is parallel to the vectors

2\hat{j} + 3\hat{k}

and

4\hat{j} - 3\hat{k}

and that

P_2

is parallel to

\hat{j} - \hat{k}

and

3\hat{i} + 3\hat{j}

, then the angle between vector

\mathbf{A}

and a given vector

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

is a.

\frac{\pi}{2}

\frac{\pi}{4}

\frac{\pi}{6}

\frac{3\pi}{4}