Three Dimensional Geometry Question 377
Question: The direction consines of two lines are related by $ l+m+n=0 $ $ al^{2}+bm^{2}+cn^{2}=0 $ . The lines are parallel if
Options:
A) $ a+b+c=0 $
B) $ {a^{-1}}+{b^{-1}}+{c^{-1}}=0 $
C) $ a=b=c $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] For $ n=-(l+m) $ , the second relation gives $ al^{2}+bm^{2}+c{{(l+m)}^{2}}=0 $ or $ (a+c)l^{2}+2clm+(b+c)m^{2}=0. $ For parallel lines, the two roots must be equal
$ \Rightarrow 4c^{2}-4(b+c)(a+c)=0\Rightarrow ab+bc+ca=0 $
BETA
