Consider the following planes P: x+y-2 z+7=0 Q: x+y+2 z+2=0 R: 3 x+3 y-6 z-11=0

Q32 / 90 · JEE Main 2012 (26 May Online) · Mathematics

Consider the following planes $$ \begin{aligned} & P: x+y-2 z+7=0 \\ & Q: x+y+2 z+2=0 \\ & R: 3 x+3 y-6 z-11=0 \end{aligned} $$

A
$P$ and $R$ are perpendicular
B
$Q$ and $R$ are perpendicular
C
$P$ and $Q$ are parallel
Correct answer
D
$P$ and $R$ are parallel

Solution

Given planes are $$ \begin{aligned} & P: x+y-2 z+7=0 \\ & Q: x+y+2 z+2=0 \end{aligned} $$ and $R: 3 x+3 y-6 z-11=0$ Consider Plane $P$ and $R$. Here $a_1=1, b_1=1, c_1=-2$ and $a_2=3, b_2=3, c_2=-6$ Since, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{3}$ therefore $P$ and $R$ are parallel.

Hence, the correct answer is option: 'D'.

Relevant Questions

Let the foot of perpendicular of the point P 3 , 2 , 9 on the plane passing through the points 1 , 2 , 3 , 9 , 3 , 4 , 9 , 2 , 1 be Q , , . 15 Apr, 2023 (M)Plane in Space
Let the plane P contain the line 2 x + y - z - 3 = 0 = 5 x - 3 y + 4 z + 9 and be parallel to the line x + 2 2 = 3 - y - 4 = z - 7 5 . Then 15 Apr, 2023 (M)Plane in Space
Let the equation of plane passing through the line of intersection of the planes x + 2 y + a z = 2 and x y + z = 3 be 5 x 11 y + b z = 6 a 113 Apr, 2023 (M)Plane in Space
Let the image of the point 5 3 , 5 3 , 8 3 in the plane x - 2 y + z 2 = 0 be P . If the distance of the point Q ( 6 , - 2 , ) , 0 , from P i13 Apr, 2023 (M)Plane in Space
The plane, passing through the points ( 0 , 1 , 2 ) and ( 1 , 2 , 1 ) and parallel to the line passing through ( 5 , 1 , 7 ) and ( 1 , 1 , 113 Apr, 2023 (E)Plane in Space
Let the plane P : 4 x - y + z = 10 be rotated by an angle 2 about its line of intersection with the plane x + y - z = 4 . If is the distance12 Apr, 2023 (M)Plane in Space