Question

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

Answer 1

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 ⇒ \(\frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}\).