A vector $\overrightarrow a$ is parallel to the line of intersection of planes $P_1$ containing vectors $\hat i,\:\hat i+\hat j$ and $P_2$ conataining vectors $\hat i-\hat j,\:\hat i+\hat k$. Then the angle between $\overrightarrow a$ and $\hat i-2\hat j+2\hat k$ is?

Question

$\large(a)\:\:\frac{\pi}{4}\:\:\:\qquad\:\:(b)\:\:\frac{\pi}{3}\:\:\:\qquad\:\:(c)\:\:\frac{\pi}{6}\:\:\:\qquad\:\:(d)\:\:\frac{\pi}{2}$