JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 1, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let 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

\hat i+2\hat j+2\hat k

. If

P(a, b, c)

is the foot of perpendicular from the origin on the line L, then the value of

34(a+b+c)

is :

(1) $50$
(2) $80$
(3) $100$ Official answer
(4) $120$

Official answer

Option 3

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 6× in all

8 Apr 2026, Shift 2 · Q23Let a line $L_1$ pass through the origin and be perpendicular to the lines…MediumNumerical value
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

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.