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Question: If **a** and **b** are unit vectors such that \(\mathbf{a} \times \mathbf{b}\) is also a unit vector...

If a and b are unit vectors such that a×b\mathbf{a} \times \mathbf{b} is also a unit vector, then the angle between a and b is

A

0

B

π3\frac{\pi}{3}

C

π2\frac{\pi}{2}

D

π\pi

Answer

π2\frac{\pi}{2}

Explanation

Solution

∣a×b∣=1⇒∣sin⁡θ∣=1⇒sin⁡θ=1⇒θ=π2|\mathbf{a} \times \mathbf{b}| = 1 \Rightarrow |\sin\theta| = 1 \Rightarrow \sin\theta = 1 \Rightarrow \theta = \frac{\pi}{2}.