JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Consider a triangle ABC whose vertices are

A(0, \alpha, \alpha)

B(\alpha, 0, \alpha)

and

C(\alpha, \alpha, 0)

\alpha > 0

. Let D be a point moving on the line

x + z - 3 = 0 = y

and G be the centroid of

\Delta ABC

. If the minimum length of GD is

\sqrt{\frac{57}{2}}

, then

\alpha

is equal to __________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Perpendicular Distance from Point to Line

Same idea in other shifts

Asked 9× in all

5 Apr 2026, Shift 1 · Q13The square of the distance of the point $P(5, 6, 7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:EasySingle correct
2 Apr 2025, Shift 1 · Q13Let the vertices Q and R of the triangle PQR lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ , $\mathrm{QR}=5$ and the…MediumSingle correct
7 Apr 2025, Shift 2 · Q17Consider the lines $L_1: x-1=y-2=z$ and $L_2: x-2=y=z-1$ . Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the lines $L_1$ …MediumSingle correct
4 Apr 2024, Shift 2 · Q16Let P be the point of intersection of the lines $\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}$ and…MediumSingle correct
9 Apr 2024, Shift 2 · Q16Consider the line L passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point…HardSingle correct
6 Apr 2023, Shift 2 · Q16Let the line L pass through the point $(0, 1, 2)$ , intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the…HardSingle correct
26 Jul 2022, Shift 1 · Q14The length of the perpendicular from the point $(1,\ -2,\ 5)$ on the line passing through $(1,\ 2,\ 4)$ and parallel to the line…MediumSingle correct
31 Aug 2021, Shift 2 · Q74The distance of the point $(-1, 2, -2)$ from the line of intersection of the planes $2x+3y+2z = 0$ and $x-2y+z = 0$ is :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.