Straight LineHard
Question
Equation of the plane containing the straight line 
and perpendicular to the plane containing the straight lines 
and 
is
and perpendicular to the plane containing the straight lines and is Options
A.x - 2y + 2z + 5 = 0
B.3x + 2y - 2z = 0
C.x - 2y + z = 0
D.5x + 2y - 4z = 0
Solution
Plane 1: ax + by + cz = 0 contains line
∴ 2a + 3b + 4c = 0 ......(i)
Plane 2: a′x + b′y + c′z = 0 is perpendicular to plane containing lines
and 
∴ 3a′ + 4b′ + 2c′ = 0 and 4a′ + 2b′ + 3c′ = 0
⇒
⇒ 8a - b - 10c = 0 .......(ii)
From (i) and (ii)
⇒ Equation of plane x - 2y + z = 0.
∴ 2a + 3b + 4c = 0 ......(i)
Plane 2: a′x + b′y + c′z = 0 is perpendicular to plane containing lines
and ∴ 3a′ + 4b′ + 2c′ = 0 and 4a′ + 2b′ + 3c′ = 0
⇒
⇒ 8a - b - 10c = 0 .......(ii)
From (i) and (ii)
⇒ Equation of plane x - 2y + z = 0.
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