Three Dimensional Geometry Question 128
Question: The projection of the line $ \frac{x+1}{1}=\frac{y}{2}=\frac{z-1}{3} $ on the plane $ x-2y+z=6 $ is the line of intersection of the plane with the plane
Options:
A) $ 2x+y+2=0 $
B) $ 3x+y-z=2 $
C) $ 2x-3y+8z=3 $
D) none of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Equation of the plane through $ ( -1,0,1 ) $ is $ a(x+1)+b(y-0)+c(z-1)=0 $ …(i) Which id parallel to the given line and perpendicular to the given plane $ -a+2b+3c=0 $ …(ii) And $ a-2b+c=0 $ …(iii) From Eqs. (ii) and (iii), we get $ c=0,a=2b $ From Eq. (i), $ 2b(x+1)+by=0 $
$ \Rightarrow 2x+y+2=0 $
BETA
