Question-37 If the directed line makes an angle 45° and 60° with the X and Y-axes respectively, then the obtuse angle \theta made by the line with the Z-axis is
(A) 135^\circ
(B) 120^\circ
(C) 160^\circ
(D) 150^\circ
Answer: (B)
Explanation:
Since \cos^2\alpha+\cos^2\beta+\cos^2\gamma=1
∴ \cos^2 45^\circ+\cos^2 60^\circ+\cos^2\gamma=1
⇒ \cos^2\gamma=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4}
⇒ \cos\gamma=\pm\frac{1}{2}
⇒ \gamma=60^\circ\ \text{or}\ 120^\circ