Three Dimensional Geometry Question 352
Question: Given the line $ L:\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1} $ and the plane $ \pi :x-2y=z $ . of the following assertions, the only one that is always true is
Options:
A) L is $ \bot $ to $ \pi $
B) L lies in $ \pi $
C) L is parallel to $ \pi $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Since $ 3(1)+2(-2)+(-1)(-1)=3-4+1=0 $
$ \therefore $ Given line is $ \bot $ to the normal to the plane i.e., given line is parallel to the given plane. Also $ (1,-1,3) $ lies on the plane $ x-2y-z=0 $ if $ 1-2(-1)-3=0 $ i.e. $ 1+2-3=0 $ Which is true
$ \therefore $ L lies in plane $ \pi $ .
BETA
