Let (α, β, γ) be the image of point (8,5,7) in the line x-1/2=y+1/3=z-2/5 . Then α+β+γ is equal to

Mathematics · 3D Geometry

JEE Main 2024 — 5 April, Shift 2 — Question 9

Let $(\alpha, \beta, \gamma)$ be the image of point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$ . Then $\alpha+\beta+\gamma$ is equal to

Option A:
16
Option B:
18
Option C:
14
Correct
Option D:
20

Answer: C

Step-by-step solution

$\overrightarrow{A M} \cdot(2 \hat{i}+3 \hat{j}+5 \hat{k})=0$

$(2 \lambda-7)(2)+(3 \lambda-6)(3)+(5 \lambda-5)(5)=0$

$38 \lambda=57$

$\lambda=\frac{3}{2}$

$\mathrm{M}\left(4, \frac{7}{2}, \frac{19}{2}\right)$

$\mathrm{A}^{\prime}(0,2,12)$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Mathematics
Chapter: 3D Geometry
Topic: Vector & Cartesian forms of lines and planes

Let the point (-1, alpha, beta) lie on the line of the shortest distance between the lines x+2/-3=y-2/4=z-5/2 and x+2/-1=y+6/2=z-1/0 . Then…

Answer: C

Step-by-step solution

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