What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?

Category: QuestionsWhat is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?
Editor">Editor Staff asked 11 months ago

What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?
 
(a) a1a2 . b1b2 . c1c2 = 0
 
(b) a1a + b1b + c1c = 0
 
(c) a1a2 + b1b2 – c1c2 = 0
 
(d) a1a2 + b1b2 – c1c2 = 0
 
The question was posed to me during a job interview.
 
The doubt is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (b) a1a + b1b + c1c = 0
 
For explanation I would say: The relation between the plane ax + by +cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other is a1a + b1b + c1c = 0.