Let the line L pass through (1,1,1) and intersect the lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-4)/(2)=(z)/(1) . Then, which of the following points lies on the line L ?

Correct answer: D. (7,15,13) aligned & Dr's of AC 2 λ, 3 λ-2,4 λ & Dr's of BC μ+2,2 μ+3, μ-1 & (μ+2)/(2 λ)=(2 μ+3)/(3 λ-2)=(μ-1)/(4 λ) & 2(μ+2)=μ-1 μ=-5 & Dr's of BC 3,7,6 & equation of L x-1 3 = y-1 7 = z-1 6 aligned (7,15,13) satisfies.

JEE Main 20257 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Three Dimensional Geometry

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Three Dimensional Geometry

Let the line L pass through (1,1,1) and intersect the lines...

Let the line L pass through

(1,1,1)

and intersect the lines

\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}

and

\frac{x-3}{1}=\frac{y-4}{2}=\frac{z}{1}

. Then, which of the following points lies on the line L ?

Options

A $(4,22,7)$
B $(5,4,3)$
C $(10,-29,-50)$
D $(7,15,13)$

Correct answer

D. $(7,15,13)$

Step-by-step solution

\begin{aligned}& \text{ Dr's of } \mathrm{AC} \Rightarrow 2 \lambda, 3 \lambda-2,4 \lambda \\ & \text{ Dr's of } \mathrm{BC} \Rightarrow \mu+2,2 \mu+3, \mu-1 \\ & \Rightarrow \frac{\mu+2}{2 \lambda}=\frac{2 \mu+3}{3 \lambda-2}=\frac{\mu-1}{4 \lambda} \\ & \Rightarrow 2(\mu+2)=\mu-1 \Rightarrow \mu=-5 \\ & \Rightarrow \text{ Dr's of } \mathrm{BC} \Rightarrow 3,7,6 \\ & \Rightarrow \text{ equation of } \mathrm{L} \Rightarrow \frac{\mathrm{x}-1}{3}=\frac{\mathrm{y}-1}{7}=\frac{\mathrm{z}-1}{6}\end{aligned}

(7,15,13) \text{ satisfies. }$

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