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

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in Mathematics - Class 12 by (687k points)
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

1 Answer

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Best answer
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

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