Question

If θ be the angle between the vectors a and b and $|\mathbf{a} \times \mathbf{b}| = \mathbf{a}.\mathbf{b},$ then $\theta =$

• A. $\pi$
• B. $\frac{\pi}{2}$
• C. $\frac{\pi}{4}$
• D. 0

Answer 1

Answer: (C)

$\frac{\pi}{4}$

Answer 2

$|\mathbf{a} \times \mathbf{b}| = (\mathbf{a}.\mathbf{b}) \Rightarrow ab\sin\theta = ab\cos\theta$

$\Rightarrow \tan\theta = \frac{ab}{ab} = 1 \Rightarrow \theta = \frac{\pi}{4}$.