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The condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other.

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The condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other.

(a) integral

(b) parallel

(c) perpendicular

(d) concentric

The question was asked during an online interview.

My question is taken from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12

1 Answer

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Best answer
The correct answer is (c) perpendicular

Easiest explanation: θ = 90 degrees ⇒ cos θ

a1a2 + b1b2 – c1c2 = 0

Relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other is a1a2 + b1b2 + c1c2 = 0.

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