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

Category: QuestionsThe condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.