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}

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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
.