JEE Main2012MathematicsThree Dimensional GeometryActual

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

Options

AP and R are perpendicular
BQ and R are perpendicular
CP and Q are parallel
DP and R are parallel

Correct answer

D. P and R are parallel

Step-by-step solution

Given planes are aligned & P: x+y-2 z+7=0 & Q: x+y+2 z+2=0 aligned and R: 3 x+3 y-6 z-11=0 Consider Plane P and R . Here a₁=1, b₁=1, c₁=-2 and a₂=3, b₂=3, c₂=-6 Since, a₁ a₂ = b₁ b₂ = c₁ c₂ = 1 3 therefore P and R are parallel.

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