First slide

Vectors

Question

$\hat{u_{1}} and \hat{u_{2}}$ are two unit vectors such that $|\hat{u_{1}} + \hat{u_{2}}| = 2 |\hat{u_{1}} - \hat{u_{2}}|$ .Then the angle between $\hat{u_{1}} and \hat{u_{2}}$ is

Easy

A

$\cos^{- 1} (\frac{4}{5})$
B

$\cos^{- 1} (\frac{\sqrt{2}}{3})$
C

$\cos^{- 1} (\frac{3}{4})$
D

$\cos^{- 1} (\frac{3}{5})$

Solution

$\begin{array}{l} 1^{2} + 1^{2} + 2 .1.1. cosθ = 4 (1^{2} + 1^{2} + 2 .1.1. cosθ) \\ \Rightarrow 10 cosθ = 6 \Rightarrow θ = \cos^{- 1} (\frac{3}{5}) \end{array}$

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