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The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.

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in Mathematics - Class 12 by (687k points)
The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.

(a) 4

(b) -14

(c) 6

(d) -8

I got this question in an international level competition.

This key question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12

1 Answer

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Best answer
Correct option is (b) -14

To explain: The condition for a plane and a line are parallel to each other is a1a + b1b + c1c = 0.

5(3) + 1(-1) + k(1) = 0

K(1) = -14

K = -14

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