Mathematics

Introduction to Three Dimensional Geometry

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Consider the line L given by the equation {x-3}{2}={y-1}{1}={z

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Consider the line L given by the equation $\frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1}$ . Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?

Name: Video answer for Consider the line L given by the equation 2x−3=1y−1=1z−2. Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?
Uploaded: 2022-12-10T04:38:27.000Z
Duration: 14 min
Description: Consider the line L given by the equation 2x−3=1y−1=1z−2. Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?

(1, 1, 1)

(–1, 1, 2)

(1, 2, 2)

(1, 1, 2)

Views: 5,834 students

Updated on: Dec 10, 2022

Exam:

JEE Mains 2021 July 20 Shift 2

Text solutionVerified

Let A (2,3,–1)

Let image of A (2,3,–1) in the line mirror

\frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1}

Q (α, β, γ)

\Rightarrow (\frac{α + 2}{2}, \frac{β + 3}{2}, \frac{γ - 1}{2}) lies on \frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1}

\Rightarrow \frac{α - 4}{4} = \frac{β + 1}{2} = \frac{γ - 5}{2} \dots\dots\dots . (1)

Also

AQ ⊥

to given line L

\Rightarrow 2 (α - 2) + (β - 3) + (γ + 1) = 0

\Rightarrow 2 α + β + γ - 6 = 0

by solving (1) and (2)

we get

α = 2, β = - 2, γ = 4

\Rightarrow Q (2, - 2, 4)

Now equation of plane P which passes through Q(1,-1,5) and perpendicular to the line L is

2(x – 2) + 1 (y + 2) + 1 (z – 4) = 0

2x+y+z = 6

Hence point (1,2,2) lies in it

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Consider the line L given by the equation

\frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1}

. Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?

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Question Text	Consider the line L given by the equation $\frac{x - 3}{2} = \frac{y - 1}{1} = \frac{z - 2}{1}$ . Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?
Updated On	Dec 10, 2022
Topic	Introduction to Three Dimensional Geometry
Subject	Mathematics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	150
Avg. Video Duration	14 min

Text solutionVerified

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Consider the line L given by the equation 2x−3​=1y−1​=1z−2​. Let Q be the mirror image of the point (2,3,–1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P ?

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