Let (α, β, γ) be mirror image of the point (2,3,5) in the line x-1/2-y-2/3-z-3/4 . Then 2 α+3 β+4 γ is equal to

Mathematics · 3D Geometry

JEE Main 2024 — 31 January, Shift 2 — Question 6

Let $(\alpha, \beta, \gamma)$ be mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}-\frac{y-2}{3}-\frac{z-3}{4}$ . Then $2 \alpha+3 \beta+4 \gamma$ is equal to

Option A:
32
Option B:
33
Correct
Option C:
31
Option D:
34

Answer: B

Step-by-step solution

$\because \overrightarrow{\mathrm{PR}} \perp(2,3,4)$

$\therefore \overrightarrow{\mathrm{PR}} \cdot(2,3,4)=0$

$(\alpha-2, \beta-3, \gamma-5) \cdot(2,3,4)=0$

$\Rightarrow 2 \alpha+3 \beta+4 \gamma=4+9+20=33$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 31 January, Shift 2
Subject: Mathematics
Chapter: 3D Geometry
Topic: Vector & Cartesian forms of lines and planes

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Answer: B

Step-by-step solution

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