JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q16

Question 16 of 75 in this shift, Maths question 16 of 25, Section A.

If the equation of the line passing through the point

\left(0,-\frac{1}{2},0\right)

and perpendicular to the lines

\vec{r}=\lambda(\hat{i}+a\hat{j}+b\hat{k})

and

\vec{r}=(\hat{i}-\hat{j}-6\hat{k})+\mu(-b\hat{i}+a\hat{j}+5\hat{k})

\frac{x-1}{-2}=\frac{y+4}{d}=\frac{z-c}{-4}

, then

a+b+c+d

is equal to :

(1)10
(2)12
(3)13
(4)14Official answer

Official answer

Option 4

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

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