JEE Math Practice Question

A vector $$\vec{a}$$ 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 $$\hat{i}-\hat{j}, \hat{i}+\hat{k}$$. The obtuse angle between $$\vec{a}$$ and the vector $$\vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$$ is :

1. A.$$\frac{3 \pi}{4}$$
2. B.$$\frac{2 \pi}{3}$$
3. C.$$\frac{4 \pi}{5}$$
4. D.$$\frac{5 \pi}{6}$$