JEE Main 2026 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2026, Shift 2, Maths Q23

Question 23 of 75 in this shift, Maths question 23 of 25, Section B.

Let a line

L_1

pass through the origin and be perpendicular to the lines

L_2 : \vec{r} = (3 + t)\hat{i} + (2t - 1)\hat{j} + (2t + 4)\hat{k}

and

L_3 : \vec{r} = (3 + 2s)\hat{i} + (3 + 2s)\hat{j} + (2 + s)\hat{k}

t, s \in \mathbf{R}

. If

(a, b, c)

a \in \mathbf{Z}

, is the point on

L_3

at a distance of

\sqrt{17}

from the point of intersection of

L_1

and

L_2

, then

(a + b + c)^2

is equal to ________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Line Perpendicular to Two Given Lines

Same idea in other shifts

Asked 7× in all

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
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
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
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
11 Apr 2023, Shift 1 · Q22Let a line $l$ pass through the origin and be perpendicular to the lines…HardNumerical value
25 Feb 2021, Shift 2 · Q88A line ‘ $l$ ’ passing through origin is perpendicular to the lines $l_1: \vec{r} = (3+t)\hat{i} + (-1+2t)\hat{j} + (4+2t)\hat{k}$ …HardNumerical 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.