Three Dimensional Geometry Question 290
Question: What are the direction ratios of the line determined by the planes $ x-y+2z=1 $ and $ x+y-z=3 $ ?
Options:
A) (-1, 3, 2)
B) (-1, -3, 2)
C) (2, 1, 3)
D) (2, 3, 2)
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The intersection of given plane is $ x-y+2z-1+\lambda (x+y-z-3)=0 $
$ \Rightarrow x(1+\lambda )+y(\lambda -1)+z(2-\lambda )-3\lambda -1=0 $ DR?s of normal to the above plane is $ (1+\lambda ,\lambda -1,2-\lambda ) $ By taking option (a) $ -1(1+\lambda )+3(\lambda -1)+2(2-\lambda )=0 $
$ \Rightarrow -1-\lambda +3\lambda -3+4-2\lambda =0 $
$ \Rightarrow 0=0 $ Which is true.
BETA
