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

Category: QuestionsThe plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.
Editor">Editor Staff asked 11 months ago

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
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 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