Q 11-03-109JEE MainJEE Main 2022 (25 Jun, Shift 1)Medium
Which of the following relations is true for two unit vectors $\hat A$ and $\hat B$ making an angle $\theta$ to each other?
Answer: (B) $|\hat A - \hat B| = |\hat A + \hat B|\tan\dfrac\theta2$
For unit vectors at angle $\theta$:
$$|\hat A + \hat B| = \sqrt{2 + 2\cos\theta} = 2\cos\frac\theta2,\qquad |\hat A - \hat B| = \sqrt{2 - 2\cos\theta} = 2\sin\frac\theta2$$
Hence $|\hat A - \hat B| = |\hat A + \hat B|\tan\dfrac\theta2$.
Solution by Sreeraj P, M.Sc Physics