The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.

Category: QuestionsThe planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
Editor">Editor Staff asked 11 months ago

The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
 
(a) 4
 
(b) 2
 
(c) 6
 
(d) 8
 
The question was posed to me in exam.
 
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

Correct choice is (b) 2
 
The best I can explain: 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.
 
5(1) + 1(1) + 3(-k) = 0
 
-3k = -6
 
K = 2