JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 31 August 2021, Shift 1, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

The 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

from the point

(-1, -1, 2)

is __________.

Official answer

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
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

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.