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BITSAT 2019

Exam: BITSAT
Year: 2019
Subject: Mathematics
Chapter: Three Dimensional Geometry

BITSAT 2019 · Mathematics · Three Dimensional Geometry

An equation of plane parallel to plane x - 2y + 2z - 5 = 0 and at a...

An equation of plane parallel to plane

x - 2y + 2z - 5 = 0

and at a unit distance from the origin is

Options

A $x - 2y + 2z = 3$
B $x - 2y + 2z + 1 = 0$
C $x - 2y + 2z - 1 = 0$
D $x - 2y + 2z + 5 = 0$

Correct answer

A. $x - 2y + 2z = 3$

Step-by-step solution

Equation of plane parallel to the plane&

$x - 2y + 2z - 5 = 0$ is $x - 2y + 2z + \lambda = 0$

Since, this plane is unit distance from origin

$∴ 1 = \left|\dfrac{λ}{1 + 4 + 4}\right|$

$| \lambda | = 3 ⇒ \lambda = \pm 3$

$∴$ Equation of plane is

$x - 2y + 2z = 3$

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