If θ is the angle between two unit vectors $\hat a$ and $\hat b$ then $|\hat a-\hat b|=$

$2\sin\frac{θ}{2}$

The correct answer is Option (2) → $2\sin\frac{θ}{2}$

Let $\hat{a}$ and $\hat{b}$ be two unit vectors with angle $\theta$ between them.

Then,

$|\hat{a} - \hat{b}| = \sqrt{ (\hat{a} - \hat{b}) \cdot (\hat{a} - \hat{b}) }$

$= \sqrt{ |\hat{a}|^2 + |\hat{b}|^2 - 2 \hat{a} \cdot \hat{b} }$

$= \sqrt{1 + 1 - 2\cos\theta} = \sqrt{2(1 - \cos\theta)}$

Using the identity: $1 - \cos\theta = 2\sin^2\left(\frac{\theta}{2}\right)$

$\Rightarrow |\hat{a} - \hat{b}| = \sqrt{2 \cdot 2\sin^2\left(\frac{\theta}{2}\right)} = \sqrt{4\sin^2\left(\frac{\theta}{2}\right)} = 2\sin\left(\frac{\theta}{2}\right)$