Three Dimensional Geometry Question 269
Question: The equation of the plane containing the line of intersection of the planes $ 2x-y=0 $ and $ y-3z=0 $ and perpendicular to the plane $ 4x+5y-3z-8=0 $ is
Options:
A) $ 28x-17y+9z=0 $
B) $ 28x+17y+9z=0 $
C) $ 28x-17y+9x=0 $
D) $ 7x-3y+z=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Equation of plane containing the line of intersection of planes is, $ (2x-y)+\lambda ,(y-3z)=0 $ ??(i) Also, plane (i) is perpendicular to $ 4x+5y-3z-8=0 $
$ \therefore 4,(2)+5,(\lambda -1)-3,(-3\lambda )=0 $
$ \Rightarrow 14\lambda =-,3\Rightarrow \lambda =-\frac{3}{14} $ Put the value of $ \lambda $ in (i), we get $ 28x-17y+9z=0 $ , which is the required plane.
BETA
