Line (x + 1)λ = y - 1 = (z + 2)- 4 is perpendicular to 2x + 2y - 8z + 5 = 0 , then λ is

Correct answer: A. 1 When line x - x _ 1 a1 = y - y _ 1 b1 = z - z _ 1 c1 is perpendicular to plane ax + by + cz + d = 0 , then (a1)/(a) = (b1)/(b) = (c1)/(c) ∴ (λ)/(2) = (1)/(2) = (- 4)/(- 8) ⇒ λ = 1 Hence, option (a) is correct.

BITSAT 2018

Exam: BITSAT
Year: 2018
Subject: Mathematics
Chapter: Three Dimensional Geometry

BITSAT 2018 · Mathematics · Three Dimensional Geometry

Line (x + 1)λ = y - 1 = (z + 2)- 4 is perpendicular to 2x + 2y - 8z...

Line

\left(x + 1\right)\lambda = y - 1 = \left(z + 2\right)- 4

is perpendicular to

2x + 2y - 8z + 5 = 0

, then

\lambda

Options

A $1$
B $- 4$
C $- 5$
D $- 3$

Correct answer

A. $1$

Step-by-step solution

When line $\dfrac{x - {x}_{1}}{a1} = \dfrac{y - {y}_{1}}{b1} = \dfrac{z - {z}_{1}}{c1}$ is perpendicular to plane $ax + by + cz + d = 0$ , then

$\dfrac{a1}{a} = \dfrac{b1}{b} = \dfrac{c1}{c}$

$∴ \dfrac{λ}{2} = \dfrac{1}{2} = \dfrac{- 4}{- 8}$

$⇒ \lambda = 1$

Hence, option (a) is correct.

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