Two vectors → A and → B have equal magnitudes. If magnitude of → A...

Given: $\left|\overset{\to}{A} + \overset{\to}{B}\right| = 2\left|\overset{\to}{A} - \overset{\to}{B}\right| </p><p>We have, </p><p>${A}^{2} + {A}^{2} + 2{A}^{2}cos\theta = 4\left({A}^{2} + {A}^{2} - 2{A}^{2}cos\theta\right)$</p><p>Simplifying we get </p><p>$2{A}^{2} + 2{A}^{2}cos\theta = 8{A}^{2} - 8{A}^{2}cos\theta$</p><p>$⇒ 1 + cos\theta = 4 - 4cos\theta$</p><p>$⇒ 5cos\theta = 3 ⇒ cos\theta = \dfrac{3}{5} ⇒ \theta = \cos^{- 1}\dfrac{3}{5}$