If a line makes 45°, 60° with positive direction of axes x and y then the angle it makes with the z-axis is :

Question 110 of 162

45°, 60°

(a)

30°

(b)

90°

(c)

45°

(d)

60°

Puducherry TnboardTamil Nadu HSC (DGE) Board 2017MCQ· 1mImportance★★★★★

68% · 110/162 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Using $\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1$ with $\alpha=45°,\beta=60°$ gives $\gamma=60°$ .

For any line in space, its direction cosines with the coordinate axes satisfy $\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1$ .
$\cos45°=\dfrac{1}{\sqrt2}\Rightarrow\cos^245°=\dfrac12$ ; $\cos60°=\dfrac12\Rightarrow\cos^260°=\dfrac14$ .
So $\cos^2\gamma = 1-\dfrac12-\dfrac14=\dfrac14 \Rightarrow \cos\gamma=\pm\dfrac12$ . …

Q.If a line makes $45°, 60°$ with positive direction of axes $x$ and $y$ then the angle it makes with the $z$ -axis is :