First slide

Vectors

Question

The angles which a vector $\hat{i} + \hat{j} + \sqrt{2} k$ makes with X, Y and Z axes respectively are

Moderate

A

$60^{0}, 60^{0}, 60^{0}$
B

$45^{0}, 45^{0}, 45^{0}$
C

$60^{0}, 60^{0}, 45^{0}$
D

$45^{0}, 45^{0}, 60^{0}$

Solution

$\vec{R} = \hat{i} + \hat{j} + \sqrt{2} \hat{k}$
comparing the given vector with $\vec{R} = R_{x} \hat{i} + R_{y} \hat{j} + R_{s} \hat{k}$
$R_{x} = 1, R_{y} = \sqrt{2} and | \vec{R} | = \sqrt{R_{x}^{2} + R_{y}^{2} + R_{z}^{2}} = 2$
$\cos α = \frac{R_{x}}{R} = \frac{1}{2} \Rightarrow α = 60^{0}$
$cosβ = \frac{R_{y}}{R} = \frac{1}{2} \Rightarrow β = 60^{0}$
$cosγ = \frac{R_{z}}{R} = \frac{1}{\sqrt{2}} \Rightarrow γ = 45^{0}$

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