What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?

Category: QuestionsWhat is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?
Editor">Editor Staff asked 11 months ago

What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?
 
(a) a1a2 . b1b2 . c1c2 = 0
 
(b) a1a2 + b1b2 + c1c2 = 0
 
(c) a1a2 + b1b2 – c1c2 = 0
 
(d) a1a2 + b1b2 – c1c2 = 0
 
I have been asked this question in my homework.
 
This is a very interesting question from Three Dimensional Geometry topic in section 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

Right answer is (b) a1a2 + b1b2 + c1c2 = 0
 
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.