If ${b} \times({a} \times {b})=\frac{2}{3}{a}$, then angle between a and b is

Question

If $\mathbf{b} \times(\mathbf{a} \times \mathbf{b})=\frac{2}{3} \mathbf{a}$, then angle between $\mathbf{a}$ and $\mathbf{b}$ is

(a) $\frac{\pi}{3}$

(b) $\frac{\pi}{6}$

(c) $\frac{\pi}{2}$

(d) None of these

Answer 1

$ \mathbf{b} \times(\mathbf{a} \times \mathbf{b})=\frac{2}{3} \mathbf{a} \Rightarrow(\mathbf{b} \cdot \mathbf{b}) \mathbf{a}-(\mathbf{b} \cdot \mathbf{a}) \mathbf{b}=\frac{2}{3} \mathbf{a}\\ \Rightarrow \quad \mathbf{a} \cdot \mathbf{b}=0 \Rightarrow \mathbf{a} \perp \mathbf{b}$

So, The correct option of this question will be (C).