Let $$a, b$$ and $$c$$ be three unit vectors such that $$a \times(b \times c)=\frac{\sqrt{3}}{2}(b+c)$$. If $$b$$ is not parallel to $$c$$, then the angle between $$a$$ and $$b$$ is

A unit vector perpendicular to both the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ is