Q 11-03-078JEE MainJEE Main 2024 (31 Jan, Shift 2)Easy
If two vectors $\vec A$ and $\vec B$ having equal magnitude $R$ are inclined at an angle $\theta$, then
Answer: (C) $|\vec A + \vec B| = 2R\cos\dfrac\theta2$
$$|\vec A + \vec B| = \sqrt{R^2 + R^2 + 2R^2\cos\theta} = R\sqrt{2(1 + \cos\theta)} = 2R\cos\frac\theta2$$
(Similarly $|\vec A - \vec B| = 2R\sin\dfrac\theta2$, so the other options are wrong.)
Solution by Sreeraj P, M.Sc Physics