JEE Main Maths · Three Dimensional Geometry

Lines in 3D in JEE Main

Name: Lines in 3D: JEE Main previous year questions
Creator: Lumi

Lines in 3D (Maths, Three Dimensional Geometry) came 39 times in 28 of the 42 JEE Main shifts Lumi analysed, across 14 distinct ideas. 34 of them came in 2024–26; it was last asked in 2026.

Questions: 39; in 28 shifts
Ideas asked: 14; 8 asked more than once
Numerical answer: 9; 23% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 31Hard 7

Format

Single correct30 Q
Numerical value9 Q

Ideas inside the topic

14 ideas

Image of a Point in a Line8 Q
Foot of the Perpendicular6 Q
Line Perpendicular to Two Given Lines6 Q
Perpendicular Distance from Point to Line4 Q
Point of Intersection Calculation3 Q
Condition for Intersection of Two Lines2 Q
Line Through Point Intersecting Two Skew Lines2 Q
Line Parallel to Vector Intersecting Two Lines2 Q
Direction Cosines Squares Identity1 Q
Distance Measured Parallel to Another Line1 Q
General Point Parameterization1 Q
Line Intersecting Two Skew Lines Parallel to a Third1 Q

Where it sits

Part of Three Dimensional Geometry, which had 84 questions in all. Lines in 3D accounts for 46% of them. In Lumi's JEE taxonomy it belongs to Vectors and 3D Geometry.

Every question

All 39 Lines in 3D questions

Newest first, each with its options and official answer.

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
5 Apr 2026, Shift 1 · Q15The square of the distance of the point of intersection of the lines…MediumSingle correct
5 Apr 2026, Shift 2 · Q14Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from…MediumSingle correct
5 Apr 2026, Shift 2 · Q15If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is…MediumSingle correct
6 Apr 2026, Shift 1 · Q15Let the image of the point $\mathrm{P}(1,6,a)$ in the line $\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}$ , $b>0$ , be…HardSingle correct
6 Apr 2026, Shift 2 · Q24Let the image of the point P $(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point…HardNumerical value
8 Apr 2026, Shift 2 · Q15Let the foot of perpendicular from the point $(\lambda, 2, 3)$ on the line $\frac{x-4}{1} = \frac{y-9}{2} = \frac{z-5}{1}$ be the point…MediumSingle correct
8 Apr 2026, Shift 2 · Q23Let a line $L_1$ pass through the origin and be perpendicular to the lines…MediumNumerical value
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
2 Apr 2025, Shift 2 · Q14If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$ , then…MediumSingle correct
3 Apr 2025, Shift 1 · Q15Let a line passing through the point $(4, 1, 0)$ intersect the line $\mathrm{L}_1 : \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ at the…HardSingle correct
3 Apr 2025, Shift 2 · Q14Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y$ - and $z$ -axes, respectively, is half of the angle…MediumSingle correct
3 Apr 2025, Shift 2 · Q15The distance of the point $(7, 10, 11)$ from the line $\frac{x-4}{1} = \frac{y-4}{0} = \frac{z-2}{3}$ along the line…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
7 Apr 2025, Shift 1 · Q13Let the line L pass through $(1, 1, 1)$ and intersect the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and…MediumSingle correct
7 Apr 2025, Shift 2 · Q16If the equation of the line passing through the point $\left(0,-\frac{1}{2},0\right)$ and perpendicular to the lines…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
6 Apr 2024, Shift 2 · Q17Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the…HardSingle correct
9 Apr 2024, Shift 1 · Q15Let the line L intersect the lines $x-2=-y=z-1$ , $2(x+1)=2(y-1)=z+1$ and be parallel to the line…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
9 Apr 2024, Shift 2 · Q29The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$ , from the origin is…MediumNumerical value
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 Jan 2024, Shift 1 · Q29A line with direction ratios $2,1,2$ meets the lines $x=y+2=z$ and $x+2=2y=2z$ respectively at the points P and Q. If the length of the…HardNumerical value
30 Jan 2024, Shift 2 · Q17Let $L_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R}$ ,…MediumSingle correct
30 Jan 2024, Shift 2 · Q29Let a line passing through the point $(-1, 2, 3)$ intersect the lines $L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}$ at…MediumNumerical value
31 Jan 2024, Shift 1 · Q15The distance of the point $Q(0,2,-2)$ form the line passing through the point $P(5,-4,3)$ and perpendicular to the lines…MediumSingle correct
31 Jan 2024, Shift 1 · Q29Let Q and R be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y,\ z=1$ and $x=-y,\ z=-1$ respectively. If…MediumNumerical value
31 Jan 2024, Shift 2 · Q16Let $(\alpha,\beta,\gamma)$ be the mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ . Then,…MediumSingle correct
31 Jan 2024, Shift 2 · Q29A 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 $AB$ …MediumNumerical value
11 Apr 2023, Shift 1 · Q22Let a line $l$ pass through the origin and be perpendicular to the lines…HardNumerical value
13 Apr 2023, Shift 2 · Q16Let N be the foot of perpendicular from the point P $(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$ . Then the…MediumSingle correct
24 Jun 2022, Shift 1 · Q24Let a line having direction ratios $1, -4, 2$ intersect the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and…MediumNumerical value
25 Jul 2021, Shift 1 · Q69Let the foot of perpendicular from a point P(1, 2, $-1$ ) to the straight line $L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}$ be N. Let a line be…MediumSingle correct
16 Mar 2021, Shift 2 · Q61If the foot of the perpendicular from point (4, 3, 8) on the line $L_1:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}$ , $l\neq0$ is (3, 5, 7),…MediumSingle correct