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

When line x - x 1 a 1 = y - y 1 b 1 = z - z 1 c 1 is perpendicular to plane a x + b y + c z + d = 0 , then a 1 a = b 1 b = c 1 c ∴ λ 2 = 1 2 = - 4 - 8 ⇒ λ = 1 Hence, option (a) is correct.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryMiscellaneous/MixedEasy2 minPYQ_2018

MathematicsEasysingle choice

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

Options:

Answer:

Solution:

When line $\frac{x - x_{1}}{a_{1}} = \frac{y - y_{1}}{b_{1}} = \frac{z - z_{1}}{c_{1}}$ is perpendicular to plane $a x + b y + c z + d = 0$ , then

$\frac{a_{1}}{a} = \frac{b_{1}}{b} = \frac{c_{1}}{c}$

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

$\Rightarrow λ = 1$

Hence, option (a) is correct.

Stream:BITSATSubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2018

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