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?

Category: QuestionsWhat 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?
Editor">Editor Staff asked 11 months ago

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
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct choice is (c)
a
a1
=
b
b1
=
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
a
a1
=
b
b1
=
c
c1
.