JEE Mathematics

Skew Lines & Shortest Distance: JEE Questions & Solutions

26 previous-year JEE Mathematics questions on Skew Lines & Shortest Distance, each with a worked step-by-step solution.

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Previous-year questions

  1. 01Let P(α, β, γ) be the point on the line (x-1)/2 = (y+1)/(-3) = z at a distance 4√14 from the point (1,-1,0) and nearer to the origin. Then…MCQMediumJEE 2026
  2. 02The sum of all values of α, for which the shortest distance between the lines (x+1)/α=(y-2)/(-1)=(z-4)/(-α) and x/α=(y-1)/2=(z-1)/2α is √2,…MCQMediumJEE 2026
  3. 03Let L₁: (x-1)/2 = (y-2)/3 = (z-3)/4 and L₂: (x-2)/3 = (y-4)/4 = (z-5)/5 be two lines. Then which of the following points lies on the line…MCQMediumJEE 2025
  4. 04If the square of the shortest distance between the lines (x-2)/1 = (y-1)/2 = (z+3)/(-3) and (x+1)/2 = (y+3)/4 = (z+5)/(-5) is m/n, where m…MCQMediumJEE 2025
  5. 05The line L₁ is parallel to the vector a = -3i + 2j + 4k and passes through the point (7, 6, 2), and the line L₂ is parallel to the vector b…MCQMediumJEE 2025
  6. 06Line L₁ passes through the point (1, 2, 3) and is parallel to z-axis. Line L₂ passes through the point (λ, 5, 6) and is parallel to y-axis.…MCQMediumJEE 2025
  7. 07Let the shortest distance between the lines (x-3)/3 = (y-α)/(-1) = (z-3)/1 and (x+3)/(-3) = (y+7)/2 = (z-β)/4 be 3√30. Then the positive…MCQMediumJEE 2025
  8. 08Let the values of p, for which the shortest distance between the lines (x + 1)/3 = y/4 = z/5 and r = (p i + 2 j + k) + λ (2 i + 3 j + 4 k)…MCQMediumJEE 2025
  9. 09If the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and x/1 = y/α = (z-5)/1 is 5/√6, then the sum of all possible values…MCQMediumJEE 2025
  10. 10Let the values of λ for which the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-λ)/3 = (y-4)/4 = (z-5)/5 is 1/√6…MCQMediumJEE 2025
  11. 11The shortest distance between the lines (x - 4)/1 = (y + 1)/2 = z/(-3) and (x - λ)/2 = (y + 1)/4 = (z - 2)/(-5) is 6/√5. The sum of all…MCQMediumJEE 2024
  12. 12Let O be the origin, and M and N be the points on the lines: (x-5)/4 = (y-4)/1 = (z-5)/3 and (x+8)/12 = (y+2)/5 = (z+11)/9, respectively,…NVAMediumJEE 2024
  13. 13If d₁ is the shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z - 6, and d₂ is the shortest distance between the…NVAMediumJEE 2024
  14. 14If the shortest distance between the lines (x + √6)/2 = (y - √6)/3 = (z - √6)/4 and (x - λ)/3 = (y - 2√6)/4 = (z + 2√6)/5 is 6, then the…NVAMediumJEE 2023
  15. 15The shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z - 6 is:MCQMediumJEE 2023
  16. 16If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line (x-1)/2 = (y+1)/(-1) = (z-2)/0 is α,…NVAMediumJEE 2023
  17. 17Shortest distance between the lines (x-1)/2 = (y+8)/(-7) = (z-4)/5 and (x-1)/2 = (y-2)/1 = (z-6)/(-3) is:MCQMediumJEE 2023
  18. 18The line ℓ₁ passes through the point (2, 6, 2) and is perpendicular to the plane 2x + y - 2z = 10. Then the shortest distance between the…MCQMediumJEE 2023
  19. 19Let the shortest distance between the lines L: (x - 5)/2 = (y - λ)/0 = (z + 1)/(-1), λ ≥ 0 and L₁: x + 1 = y - 1 = 4 - z be 2√6. If (α, β,…MCQMediumJEE 2023
  20. 20The shortest distance between the lines (x-5)/1 = (y-2)/2 = (z-4)/(-3), (x+3)/1 = (y+5)/4 = (z-1)/(-5) is:MCQMediumJEE 2023
  21. 21One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units…MCQMediumJEE 2023
  22. 22The shortest distance between the lines (x-4)/4 = (y+2)/5 = (z+3)/3 and (x-1)/3 = (y-3)/4 = (z-4)/2 is:MCQMediumJEE 2023
  23. 23The shortest distance between the lines (x + 2)/1 = y/(-2) = (z - 5)/2 and (x - 4)/1 = (y - 1)/2 = (z + 3)/0 is:MCQMediumJEE 2023
  24. 24The distance of the point (-1, 2, 3) from the plane r · (i - 2j + 3k) = 10, measured parallel to the line of shortest distance between the…MCQMediumJEE 2023
  25. 25The line, that is coplanar to the line (x+3)/(-3) = (y-1)/1 = (z-5)/5, is:MCQMediumJEE 2023
  26. 26Let S be the set of all values of λ, for which the shortest distance between the lines (x-λ)/0=(y-3)/4=(z+6)/1 and (x+λ)/3=y/(-4)=(z-6)/0…MCQMediumJEE 2023

Frequently asked questions

Our bank has 26 previous-year JEE Mathematics questions tagged to Skew Lines & Shortest Distance, drawn from JEE papers between 2023 and 2026, including 2 from 2026 alone. Each comes with a full step-by-step solution.

Skew Lines & Shortest Distance is rated Advanced overall for JEE Mathematics. The PYQs on this page break down as 26 medium.

Of the 26 previous-year questions on Skew Lines & Shortest Distance, 22 are multiple-choice (MCQ) and 4 are numerical-value (NVA) questions.

Based on recent paper analysis, Skew Lines & Shortest Distance is worth about 2 marks in JEE Main. It sits in Three-Dimensional Geometry, a Class 12 Mathematics chapter.

More Three-Dimensional Geometry topics

Equation of Line in 3D57Equation of Plane39Coordinates in 3D6Direction Cosines & Ratios3

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