Three Dimensional Geometry Question 371
Question: A line makes angles, $ \theta ,\phi $ and $ \psi $ with x, y, z axes respectively. Consider the following:
- $ {{\sin }^{2}}\theta +{{\sin }^{2}}\phi ={{\cos }^{2}}\psi $
- $ {{\cos }^{2}}\theta +{{\cos }^{2}}\phi ={{\sin }^{2}}\psi $
- $ {{\sin }^{2}}\theta +{{\cos }^{2}}\phi ={{\cos }^{2}}\psi $ Which of the above is/are correct?
Options:
A) 1 only
B) 2 only
C) 3 only
D) 2 and 3
Show Answer
Answer:
Correct Answer: B
Solution:
[b] If a line makes angle $ \theta ,\phi $ and $ \psi $ with x, y, z Axes respectively, then $ {{\cos }^{2}}\theta +{{\cos }^{2}}\phi +{{\cos }^{2}}\psi =1 $
$ \Rightarrow {{\cos }^{2}}\theta +{{\cos }^{2}}\phi =1-{{\cos }^{2}}\psi $
$ \Rightarrow {{\cos }^{2}}\theta +{{\cos }^{2}}\phi ={{\sin }^{2}}\psi $
$ \therefore $ Statement (2) is correct.
BETA
