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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Three Dimensional Geometry

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Three Dimensional Geometry

Let (α, β, γ) be the image of the point (8,5,7) in the line...

Let (α,β,γ)(\alpha, \beta, \gamma) be the image of the point (8,5,7)(8,5,7) in the line x−12=y+13=z−25\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}. Then α+β+γ\alpha+\beta+\gamma is equal to :Let (α, β, γ) be the image of the point (8,5,7) in the line (x-1)/(2)=(y+1)/(3)=(z-2)/(5) . Then α+β+γ is equal to :

Options

  1. A16
  2. B20
  3. C14
  4. D18

Correct answer

C. 14

Step-by-step solution

Let (α, β, γ) be the image of the point (8,5,7) in the line (x-1)/(2)=(y+1)/(3)=(z-2)/(5) . Then α+β+γ is equal to :
AM→⋅(2i^+3j^+5k^)=0(2λ−7)(2)+(3λ−6)(3)+(5λ−5)(5)=038λ=57λ=32M(4,72,192)A′(0,2,12)\begin{aligned} & \overrightarrow{\mathrm{AM}} \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{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)\end{aligned}
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