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 perpendicular to each other?

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

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

(c) \(\frac {a}{a1} = \frac{b}{b1} = \frac{c}{c1}\)

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

I got this question in an online interview.

I'm obligated to ask this question of Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Correct choice is (c) \(\frac {a}{a1} = \frac{b}{b1} = \frac{c}{c1}\)

To explain I would say: θ = 90 degrees

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 perpendicular to each other is \(\frac {a}{a1} = \frac{b}{b1} = \frac{c}{c1}\).