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QJEEM24Mae8a1: JEE Main 2024 Mathematics - Class 12 JEEM24Mae8a1 Solution: Let be the mirror image of the point in the line . Then, is…

Let (α,β,γ)(\alpha, \beta, \gamma) be the mirror image of the point (2,3,5)(2,3,5) in the line x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} . Then, 2α+3β+4γ2 \alpha+3 \beta+4 \gamma is equal to

Multiple Choice Options

  • A 32
  • B 31
  • C 33
  • D 34

Step-by-Step Verified Solution

JEE Main 2024 (Online) 31st January Evening Shift Mathematics - 3D Geometry Question 50 English Explanation

amp;∵PR→⊥(2,3,4)amp;∴PR→⋅(2,3,4)=0amp;(α−2,β−3,γ−5)⋅(2,3,4)=0amp;⇒2α+3β+4γ=4+9+20=33\begin{aligned}& \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\end{aligned}

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