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JEE Main 202528 JanuaryMorning Shift

Exam: JEE Main
Year: 2025
Date: 28 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Three Dimensional Geometry

JEE Main 2025 · 28 January · Morning Shift · Mathematics · Three Dimensional Geometry

If the image of the point (4,4,3) in the line...

If the image of the point

(4,4,3)

in the line

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

is

(\alpha, \beta, \gamma)

, then

\alpha+\beta+\gamma

is equal to If the image of the point (4,4,3) in the line (x-1)/(2)=(y-2)/(1)=(z-1)/(3) is (α, β, γ) , then α+β+γ is equal to

If the image of the point (4,4,3) in the line (x-1)/(2)=(y-2)/(1)=(z-1)/(3) is (α, β, γ) , then α+β+γ is equal to

Options

A9
B12
C7
D8

Correct answer

A. 9

Step-by-step solution

If the image of the point (4,4,3) in the line (x-1)/(2)=(y-2)/(1)=(z-1)/(3) is (α, β, γ) , then α+β+γ is equal to

Let coordinate of

R=(2 r+1, r+2,3 r+1)

\because \quad P R

is perpendicular to given line.

\therefore(2 r-3) \cdot 2+(r-2) \cdot 1+(3 r-2) \cdot 3=0

\therefore r=1

\therefore

Coordinate of

R=(3,3,4)

\therefore \quad(\alpha, \beta, \gamma)=(2,2,5)

\therefore \alpha+\beta+\gamma=9

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