Three Dimensional Geometry Question 255
Question: The equation of the plane passing through the points $ (1,-3,-2) $ and perpendicular to planes $ x+2y+2z=5 $ and $ 3x+3y+2z=8 $ , is
[AISSE 1987]
Options:
A) $ 2x-4y+3z-8=0 $
B) $ 2x-4y-3z+8=0 $
C) $ 2x+4y+3z+8=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ l+2m+2n=0,,3l+3m+2n=0 $ , $ l^{2}+m^{2}+n^{2}=1, $ we get l, m, n from these equations and then putting the values in $ l(x-1)+m(y+3) $ $ +n(z+2)=0, $ we get the required result.
Trick: Checking conversely,
$ 2,(1)-4,(-3) $ $ +3(-2)-8=0, $
So, it passes through given point.
$ 1(2)+2(-4)+2(3)=0, $
So, it is perpendicular to $ x+2y+2z=5 $ .
$ 3(2)+3(-4)+2(3)=0, $
So, it is perpendicular to $ 3x+3y+2z=8. $
BETA
