First slide

Vectors

Question

The angle $θ$ between the vector $p = \hat{i} + \hat{j} + \hat{k}$ and unit vector along X-axis is

Moderate

A

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

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

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

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

Solution

The angle between, $p = \hat{i} + \hat{j} + \hat{k}$
and X-axis, x = $\hat{i}$ is given by
$\cos θ = \frac{p \cdot x}{| p | | x |} = \frac{(\hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i})}{\sqrt{1^{2} + 1^{2} + 1^{2}} \cdot \sqrt{1^{2}}} = \frac{1}{\sqrt{3}}$
$∴$ $θ = \cos^{- 1} (\frac{1}{\sqrt{3}})$

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