Published by:
CGP EDU Academic Team
Published on: August 14, 2026
LetP 1 : 2x + y + z + 1 = 0, P 2 :2x - y + z + 3 = 0 and P 3 :2x + 3y + z + 5 = 0 be three planes, then the distance of the line of intersection of planes P 1 = 0 and P 2 = 0 from the plane P 3 = 0 is
A
units
B
units
C
units
D
units
Text Solution
Verified by ExpertsThe correct answer is:
B
units
A vector normal to P 1 = 0 is 
A vector normal to P 2 = 0 is 
Hence, the line of intersection is parallel to 
And for point of intersection Put z = 0 in
P 1 = 0 and P 2 = 0, i.e.
2x+y+l = 0
2x-y+3= 0
4x+4=0
and 
So point is (-1,1,0)
Equation of the line of intersection is
The line is parallel to P 3 = 0
Hence, distance 
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