Q69 / 150 · MHT CET 2018 · Mathematics

If a line makes angles $120^{o}$ and $60^{o}$ with the positive directions of $X$ and $Z$ axes respectively then the angle made by the line with positive $Y -$ axis is

A
$150^{o}$
B
$60^{o}$
Correct answer
C
$135^{o}$
D
$120^{o}$

Solution

\cos^{2} β = 1 - \cos^{2} α - \cos^{2} γ

= 1 - \cos^{2} (120^{o}) - \cos^{2} (60^{o})

= 1 - \frac{1}{4} - \frac{1}{4}

= 1 - \frac{1}{2}

\cos β = \pm \frac{1}{\sqrt{2}}

β = 135^{o}, 45^{o}

Hence, the correct answer is option: 'C'.

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