JEE Main 2025 — Three Dimensional Geometry Question with Solution
JEE Main 2025 (3 Apr Shift 1)
Question
Let a line passing through the point intersect the line at the point and the line at the point .
Then is equal to
Then is equal to
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
$\begin{aligned}
& 2 p q-2 p-3 q+3=3 p q+6 p+q+2 \\ & \mathrm{pq}+\mathrm{rp}+4 \mathrm{q}-1=0 \\ & 12 p-3 p q+4-q=4 p q+3 q-4 p-3 \\ & 7 p q-16 p+4 q-7=0 \\ & 8 p-2 p q-12+3 q=4 p q+8 p+3 q+6 \\ & 6 \mathrm{pq}=-18 \quad \therefore \mathrm{pq}=-3 \\ & 8 p+4 q=4 \quad \Rightarrow 2 p+q=1 \\ & -21-16 p+4 q-7 \quad \Rightarrow 4 p-q=-7 \\ & 16 \mathrm{p}-4 \mathrm{q}=-28 \quad \therefore \mathrm{p}=-1, \mathrm{q}=3 \\ & \mathrm{~A}(-1,-1,-1) \quad \mathrm{B}(9,3,1)
\end{aligned}\left|\begin{array}{ccc}1 & 0 & 1 \\ -1 & -1 & -1 \\ 9 & 3 & 1\end{array}\right|=\left|\begin{array}{ccc}0 & -1 & 0 \\ -1 & -1 & -1 \\ 9 & 3 & 1\end{array}\right|=1(-1+9)=8$
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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.