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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

The distance of the point Q(0,2,−2)Q(0,2,-2) form the line passing through the point P(5,−4,3)P(5,-4,3) and perpendicular to the lines r⃗=(−3i^+2k^)+λ(2i^+3j^+5k^), λ∈R\vec{r}=\left(-3\hat{i}+2\hat{k}\right)+\lambda\left(2\hat{i}+3\hat{j}+5\hat{k}\right),\ \lambda\in\mathbb{R} and r⃗=(i^−2j^+k^)+μ(−i^+3j^+2k^), μ∈R\vec{r}=\left(\hat{i}-2\hat{j}+\hat{k}\right)+\mu\left(-\hat{i}+3\hat{j}+2\hat{k}\right),\ \mu\in\mathbb{R} is :
  1. (1)86\sqrt{86}
  2. (2)74\sqrt{74}Official answer
  3. (3)54\sqrt{54}
  4. (4)20\sqrt{20}

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
  1. 2 Apr 2026, Shift 1 · Q15Let a line L passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i+2\hat j+\hat k and…MediumSingle correct
  2. 8 Apr 2026, Shift 2 · Q23Let a line L1L_1 pass through the origin and be perpendicular to the lines…MediumNumerical value
  3. 7 Apr 2025, Shift 2 · Q16If the equation of the line passing through the point (0,−12,0)\left(0,-\frac{1}{2},0\right) and perpendicular to the lines…MediumSingle correct
  4. 30 Jan 2024, Shift 2 · Q17Let L1:r⃗=(i^−j^+2k^)+λ(i^−j^+2k^),λ∈RL_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R},…MediumSingle correct
  5. 11 Apr 2023, Shift 1 · Q22Let a line ll 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.