Question

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

Answer 1

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.