Three-Dimensional-Geometry Question 418
Question: 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
[MP PET 1997]
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 $
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ \alpha =45^{o},\beta =60^{o},\gamma =? $ $ \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 \gamma =60^{o} $ or $ 120^{o} $ .
BETA
