Question

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

(a) a1a2 . b1b2 . c1c2 = 0

(b) a1a2 + b1b2 + c1c2 = 0

(c) a1a2 + b1b2 – c1c2 = 0

(d) a1a2 + b1b2 – c1c2 = 0

I have been asked this question in my homework.

This is a very interesting question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Right answer is (b) a1a2 + b1b2 + c1c2 = 0

Explanation: θ = 90 degrees ⇒ cos θ

a1a2 + b1b2 – c1c2 = 0

Relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other is a1a2 + b1b2 + c1c2 = 0.