First slide

Direction ratios and direction cosines

Question

A line makes an angle of $\frac{π}{4}$ with the positive directions of each of $y -$ and $z -$ axes. Then the angle that the line makes with the positive direction of
$x -$ axis, is

Very Easy

A

$π$
B

$\frac{π}{4}$
C

$\frac{π}{6}$
D

$\frac{π}{2}$

Solution

If $α, β, γ$ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$
Given $β = \frac{π}{4}, γ = \frac{π}{4}$
Hence, $\cos^{2} α + \frac{1}{2} + \frac{1}{2} = 1 \Rightarrow \cos γ = 0$
Therefore, $γ = \frac{π}{2}$

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