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BITSAT 2021

Exam: BITSAT
Year: 2021
Subject: Mathematics
Chapter: Three Dimensional Geometry

BITSAT 2021 · Mathematics · Three Dimensional Geometry

A line makes angles of 45^ ^ and 60^ ^ with the positive axes of X...

A line makes angles of

45^{{}^{\circ}}

and

60^{{}^{\circ}}

with the positive axes of

X

and

Y

respectively. The angle made by the same line with the positive axis of

Z

, is

Options

A $30^{{}^{\circ}}$ or $60^{{}^{\circ}}$
B $60^{{}^{\circ}}$ or $90^{{}^{\circ}}$
C $90^{{}^{\circ}}$ or $120^{{}^{\circ}}$
D $60^{{}^{\circ}}$ or $120^{{}^{\circ}}$

Correct answer

D. $60^{{}^{\circ}}$ or $120^{{}^{\circ}}$

Step-by-step solution

Given \alpha=45^{{}^{\circ}}, \beta=60^{{}^{\circ}}, \gamma=?

\begin{array}{l} \because \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\ \therefore \cos ^{2} \gamma=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\ \Rightarrow \mathrm{y}=60^{{}^{\circ}} \text{ or } 120^{{}^{\circ}} \end{array}

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