JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q75

Question 75 of 90 in this shift, Maths question 15 of 30, Section A.

The equation of a line passing through the point

(2,-1,1)

and the point of intersection of the lines

2x-y-4=0=y+2z

and

x+3z=0=2x+5z-1

, is

(1) $\frac{x-2}{1}=\frac{y+1}{-3}=\frac{z-1}{2}$
(2) $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z-1}{-2}$ Official answer
(3) $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z-1}{2}$
(4) $\frac{x-2}{-1}=\frac{y+1}{3}=\frac{z-1}{2}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Point of Intersection Calculation

Same idea in other shifts

Asked 8× in all

2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ …MediumSingle correct
4 Apr 2025, Shift 2 · Q15Let A be the point of intersection of the lines $L_1:\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}$ and…MediumSingle correct
5 Apr 2024, Shift 1 · Q17Let d be the distance of the point of intersection of the lines $\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}$ and…MediumSingle correct
29 Jan 2024, Shift 1 · Q16Let PQR be a triangle with $R(-1,4,2)$ . Suppose $M(2,1,2)$ is the mid point of PQ. The distance of the centroid of $\Delta PQR$ from the…MediumSingle correct
10 Apr 2023, Shift 2 · Q15Let the line $\frac{x}{1} = \frac{6-y}{2} = \frac{z+8}{5}$ intersect the lines $\frac{x-5}{4} = \frac{y-7}{3} = \frac{z+2}{1}$ and…HardSingle correct
29 Jul 2022, Shift 1 · Q23Let a line with direction ratios $a, -4a, -7$ be perpendicular to the lines with direction ratios $3, -1, 2b$ and $b, a, -2$ . If the point…HardNumerical value
31 Aug 2021, Shift 1 · Q87The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2x-y+z=6$ …MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.