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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 3 September 2020, Shift 1, Maths Q66

Question 66 of 75 in this shift, Maths question 16 of 25.

The lines r⃗=(i^−j^)+l(2i^+k^)\vec{r}=(\hat{i}-\hat{j})+l(2\hat{i}+\hat{k}) and r⃗=(2i^−j^)+m(i^+j^−k^)\vec{r}=(2\hat{i}-\hat{j})+\mathrm{m}(\hat{i}+\hat{j}-\hat{k})
  1. (1)intersect when l=1l=1 and m=2\mathrm{m}=2
  2. (2)intersect when l=2l=2 and m=12\mathrm{m}=\frac{1}{2}
  3. (3)intersect for all values of ll and m\mathrm{m}
  4. (4)do not intersect for any values of ll and m\mathrm{m}Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Condition for Intersection of Two Lines

Same idea in other shifts

Asked 3× in all
  1. 5 Apr 2026, Shift 1 · Q15The square of the distance of the point of intersection of the lines…MediumSingle correct
  2. 7 Apr 2025, Shift 1 · Q13Let the line L pass through (1,1,1)(1, 1, 1) and intersect the lines x−12=y+13=z−14\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} and…MediumSingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.