JEE MAIN - Mathematics (2024 - 31st January Evening Shift - No. 4)
Let $$(\alpha, \beta, \gamma)$$ be the mirror image of the point $$(2,3,5)$$ in the line $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$. Then, $$2 \alpha+3 \beta+4 \gamma$$ is equal to
32
31
33
34
Explanation
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$$\begin{aligned} & \because \overrightarrow{\mathrm{PR}} \perp(2,3,4) \\ & \therefore \overrightarrow{\mathrm{PR}} \cdot(2,3,4)=0 \\ & (\alpha-2, \beta-3, \gamma-5) \cdot(2,3,4)=0 \\ & \Rightarrow 2 \alpha+3 \beta+4 \gamma=4+9+20=33 \end{aligned}$$
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