If |a⃗| = 3, |b⃗| = (√2)/3 and a⃗ × b⃗ is a unit vector then the angle between a⃗ and b⃗ will be:

If $|\vec{a}| = 3$, $|\vec{b}| = \frac{\sqrt{2}}{3}$ and $\vec{a} \times \vec{b}$ is a unit vector then the angle between $\vec{a}$ and $\vec{b}$ will be:

(a)$\frac{\pi}{6}$
(b)$\frac{\pi}{4}$
(c)$\frac{\pi}{3}$
(d)$\frac{\pi}{2}$

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Answer

Correct option: (b)

Answer: (b) $\frac{\pi}{4}$ $|\vec{a}\times\vec{b}| = |\vec{a}||\vec{b}|\sin\theta = 1 \Rightarrow 3\cdot\frac{\sqrt{2}}{3}\sin\theta = 1$ $\sin\theta = \frac{1}{\sqrt{2}}$, so $\theta = \frac{\pi}{4}$.