JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let

L_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R}

L_2: \vec{r} = (\hat{j} - \hat{k}) + \mu(3\hat{i} + \hat{j} + p\hat{k}), \mu \in \mathbb{R}

, and

L_3: \vec{r} = \delta(\ell\hat{i} + m\hat{j} + n\hat{k}), \delta \in \mathbb{R}

be three lines such that

L_1

is perpendicular to

L_2

and

L_3

is perpendicular to both

L_1

and

L_2

. Then, the point which lies on

L_3

(1) $(1, 7, -4)$
(2) $(-1, 7, 4)$ Official answer
(3) $(1, -7, 4)$
(4) $(-1, -7, 4)$

Official answer

Option 2

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

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.