First slide

Vectors

Question

${\hat{u}}_{1} and {\hat{u}}_{2}$ are two unit vectors such that $| {\hat{u}}_{1} \times {\hat{u}}_{2} | = \sqrt{3} | {\hat{u}}_{1} . {\hat{u}}_{2} |$ . Then $| {\hat{u}}_{1} + {\hat{u}}_{2} |$ is

Easy

A

$\sqrt{2}$
B

$\sqrt{2 + \sqrt{3}}$
C

$\sqrt{3}$
D

1

Solution

$| {\hat{u}}_{1} \times {\hat{u}}_{2} | = \sqrt{3} | {\hat{u}}_{1} . {\hat{u}}_{2} | \Rightarrow 1.1 \sin θ = \sqrt{3} .1.1. \cos θ$
$∴ θ = 60^{o} =$ Angle between ${\hat{u}}_{1} and {\hat{u}}_{2}$
$∴ | {\hat{u}}_{1} + {\hat{u}}_{2} | = \sqrt{1^{2} + 1^{2} + 2.1.1. \cos 60^{o}} = \sqrt{3}$

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