What is the relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other?

Category: QuestionsWhat is the relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other?
Editor">Editor Staff asked 11 months ago

What is the relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other?
 
(a) \frac {a1}{b1} = \frac{a2}{c1} = \frac{c2}{b2}
 
(b) \frac {a1}{a2} = \frac{b1}{c2} = \frac{c1}{b2}
 
(c) \frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}
 
(d) \frac {c1}{a2} = \frac{b1}{b2} = \frac{a1}{c2}
 
This question was posed to me during an internship interview.
 
Question is taken from Three Dimensional Geometry topic in division Three Dimensional Geometry of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (c) \frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}
 
The explanation is: Relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other is a1 : b1 : c1 = a2 : b2 : c2 ⇒ \frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}.