Three Dimensional Geometry Question 104
Question: If a line makes the angle $ \alpha ,\beta ,\gamma $ with three dimensional co-ordinate axes respectively, then $ \cos 2\alpha +\cos 2\beta +\cos 2\gamma = $
[MP PET 1994, 95,99; RPET 2003; Kerala (Engg.) 2005]
Options:
A) ? 2
B) ? 1
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ \cos ,2\alpha +\cos ,2\beta +\cos ,2\gamma $ $ =2,{{\cos }^{2}}\alpha -1+2,{{\cos }^{2}}\beta -1+2,{{\cos }^{2}}\gamma -1 $ $ =2,({{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma )-3=2-3=-1. $
BETA
