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Friday, 9 October

JEE Main 2025 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 2 April 2025, Shift 2, Maths Q15

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

The line L1L_1 is parallel to the vector a⃗=−3i^+2j^+4k^\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} and passes through the point (7,6,2)(7, 6, 2) and the line L2L_2 is parallel to the vector b⃗=2i^+j^+3k^\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k} and passes through the point (5,3,4)(5, 3, 4). The shortest distance between the lines L1L_1 and L2L_2 is :
  1. (1)2138\frac{21}{\sqrt{38}}
  2. (2)2157\frac{21}{\sqrt{57}}
  3. (3)2357\frac{23}{\sqrt{57}}
  4. (4)2338\frac{23}{\sqrt{38}}Official answer

Official answer

Option 4

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Skew Lines
Idea tested
Vector Shortest Distance Formula

Same idea in other shifts

Asked 5× in all
  1. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  2. 4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines x+13=y4=z5\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5} and…MediumSingle correct
  3. 8 Apr 2024, Shift 1 · Q14If the shortest distance between the lines L1:r⃗=(2+λ)i^+(1−3λ)j^+(3+4λ)k^L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k},…MediumSingle correct
  4. 24 Jun 2022, Shift 1 · Q30If the shortest distance between the lines r⃗=(−i^+3k^)+λ(i^−aj^)\vec{r}=(-\hat{i}+3\hat{k})+\lambda(\hat{i}-a\hat{j}) and…MediumNumerical 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.