JEE Main 2024 — Three Dimensional Geometry Question with Solution
JEE Main 2024 (04 Apr Shift 2)
Question
Consider a line passing through the points and . If the mirror image of the point in the line is , then is equal to _______
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Show full solutionCorrect answer: 6
Correct answer
6
Step-by-step explanation
DR's of Line DR's of $\begin{aligned} & \mathrm{AB} \perp_{\mathrm{ar}} \mathrm{L} \Rightarrow 2-\alpha+\beta-2+2 \gamma-4=0 \\ & 2 \gamma+\beta-\alpha=4 \end{aligned}CA B$ $\begin{aligned} & \mathrm{C}\left(\frac{\alpha+2}{2}, \frac{\beta+2}{2}, \frac{\gamma+2}{2}\right) \\ & \text { DR's of PC }=\frac{\alpha}{2}: \frac{\beta-2}{2}: \frac{\gamma}{2} \\ & \text { line L } \left\lvert\, \mathrm{PC} \Rightarrow \frac{-\alpha}{2}=\frac{\beta-2}{2}=\frac{\gamma}{4}=\mathrm{K}(\text { let) }\right. \end{aligned}$ $\begin{aligned} & \alpha=-2 \mathrm{~K} \\ & \beta=2 \mathrm{~K}+2 \\ & \gamma=4 \mathrm{~K} \end{aligned}$ use in (1) value of
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This is a previous-year question from JEE Main 2024, covering the Three Dimensional Geometry chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.