JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q15

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

Let 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

\frac{x+3}{6} = \frac{3-y}{3} = \frac{z-6}{1}

at the points A and B respectively. Then the distance of the mid-point of the line segment AB from the plane

2x - 2y + z = 14

(1) $\frac{10}{3}$
(2) $\frac{11}{3}$
(3) $4$ Official answer
(4) $3$

Official answer

Option 3

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
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
4 Aug 2021, Shift 2 · Q75The 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…MediumSingle correct
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.