JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 31 January 2024, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

A line passes through

A(4,-6,-2)

and

B(16,-2,4)

. The point

P(a,b,c)

, where

a, b, c

are non-negative integers, on the line

AB

lies at a distance of 21 units, from the point

A

. The distance between the points

P(a,b,c)

and

Q(4,-12,3)

is equal to ____________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Parametric Points at Distance r

Same topic in other shifts

All Lines in 3D questions

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
2 Apr 2026, Shift 1 · Q15Let a line L passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and…MediumSingle correct
2 Apr 2026, Shift 2 · Q15Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line…MediumSingle correct
4 Apr 2026, Shift 1 · Q14A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and…MediumSingle correct
4 Apr 2026, Shift 2 · Q14If $\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line…MediumSingle correct
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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.