Three Dimensional Geometry Question 210
Question: If three mutually perpendicular lines have direction cosines $ (l_1,m_1,n_1),(l_2,m_2,n_2) $ and $ (l_3,m_3,n_3) $ , then the line having direction cosines $ l_1+l_2+l_3 $ , $ m_1+m_2+m_3 $ and $ n_1+n_2+n_3 $ make an angle of ….. with each other
Options:
A) $ 0{}^\circ $
B) $ 30{}^\circ $
C) $ 60{}^\circ $
D) $ 90{}^\circ $
Show Answer
Answer:
Correct Answer: A
Solution:
Lines are mutually perpendicular
\ $ l_1l_2+m_1m_2+n_1n_2=0,,l_2l_3+m_2m_3+n_2n_3=0 $ and $ l_1l_3+m_1m_3+n_1n_3=0 $
Therefore, $ ,\theta ={{\cos }^{-1}}[(l_1+l_2+l_3),l_1+(m_1+m_2+m_3),m_1 $ $ +(n_1+n_2+n_3)n_1] $
Þ $ \theta ={{\cos }^{-1}},[ \sum{l_1^{2}} ]={{\cos }^{-1}},(1)\Rightarrow \theta =0^{o} $
Similarly with other lines, it will make $ 0^{o} $ angle.
BETA
