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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.

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Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.

(a) 21

(b) 17

(c) 12

(d) 11

The question was posed to me in final exam.

Query is from Three Dimensional Geometry topic in chapter Three Dimensional Geometry of Mathematics – Class 12

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Correct choice is (d) 11

Easy explanation: Relation between the 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.

1(3) + 2(4) + k(-1) = 0

k(-1) = -11

k = 11

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