JEE Main 2025 — Three Dimensional Geometry Question with Solution
JEE Main 2025 (29 Jan Shift 2)
Question
Let P be the foot of the perpendicular from the point on the line . Let the line , intersect the line L at Q . Then is equal to :
Choose an option
Show full solutionCorrect option: D
Correct answer
D27
Step-by-step explanation
General point on line
is
DR's of PM are $\begin{aligned} & \Rightarrow \lambda+(-1)(-\lambda-3)+2(2 \lambda)=0 \\ & \Rightarrow 6 \lambda+3=0 \end{aligned}$
Let another line General point on line is Point of intersection of line and is $\begin{array}{l|l} \lambda+1=\mu-1 & 2 \lambda+2=\mu-2 \\ \Rightarrow \mu-\lambda=2 \ldots(1) & \Rightarrow 2 \lambda=\mu-4 \end{array}$
DR's of PM are $\begin{aligned} & \Rightarrow \lambda+(-1)(-\lambda-3)+2(2 \lambda)=0 \\ & \Rightarrow 6 \lambda+3=0 \end{aligned}$
Let another line General point on line is Point of intersection of line and is $\begin{array}{l|l} \lambda+1=\mu-1 & 2 \lambda+2=\mu-2 \\ \Rightarrow \mu-\lambda=2 \ldots(1) & \Rightarrow 2 \lambda=\mu-4 \end{array}$
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This is a previous-year question from JEE Main 2025, 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.