Three Dimensional Geometry Question 32
Question: If a line makes an angle of $ \frac{\pi }{4} $ with the positive direction of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{2} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Here $ l=\cos \frac{\pi }{4},m=\cos \frac{\pi }{4} $ Let the line make an angle $ \gamma $ with the z-axis. Then $ l^{2}+m^{2}+n^{2}=1 $ Or $ {{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\frac{\pi }{4}+{{\cos }^{2}}\gamma =1 $ Or $ \frac{1}{2}+\frac{1}{2}+{{\cos }^{2}}\gamma =1 $ Or $ 2{{\cos }^{2}}\gamma =0 $ or $ \cos \gamma =0 $ or $ \gamma =- $
BETA
