Let the point, on the line passing through the points P (1,-2,3) and Q (5,-4,7) , farther from the origin and at a distance of 9 units from the point P , be (α, β, γ) . Then α 2 +β 2 +γ 2 is equal to :

Mathematics · 3D Geometry

JEE Main 2024 — 4 April, Shift 1 — Question 16

Let the point, on the line passing through the points $\mathrm{P}(1,-2,3)$ and $\mathrm{Q}(5,-4,7)$ , farther from the origin and at a distance of 9 units from the point $P$ , be $(\alpha, \beta, \gamma)$ . Then $\alpha^{2}+\beta^{2}+\gamma^{2}$ is equal to :

Option A:
155
Correct
Option B:
3
Option C:
160
Option D:
165

Answer: A

Step-by-step solution

PQ line $\frac{x-1}{4}=\frac{y+2}{-2}=\frac{z-3}{4}$

pt $(4 \mathrm{t}+1,-2 \mathrm{t}-2,4 \mathrm{t}+3)$

distance ${ }^{2}=16 t^{2}+4 t^{2}+16 t^{2}=81$

$\mathrm{t}= \pm \frac{3}{2}$ $\operatorname{pt}(7,-5,9)$

$\alpha^{2}+\beta^{2}+\gamma^{2}=155$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: 3D Geometry
Topic: Vector & Cartesian forms of lines and planes

If the shortest distance between the lines x+2/2=y+3/3=z-5/4 and x-3/1=y-2/-3=z+4/2 is frac383 √(5) k and int 0^ k [ x^2 ]…

Answer: A

Step-by-step solution

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