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Mathematics - Three Dimensional Geometry

Practise 105 NTA Abhyas (JEE Main) questions on Three Dimensional Geometry. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Three Dimensional Geometry has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 105 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If the direction ratios of a line are 1 + λ , 2 - λ , 4 and if it makes an angle of 6 0 o with the y -axis, then the sum of the values of λ
  2. 2The distance between the point - 1 , - 5 , - 10 and the point of intersection of the line x - 2 3 = y + 1 4 = z - 2 12 with the plane x - y
  3. 3A normal line with positive direction cosines to the plane P makes equal angles with the coordinate axes. The distance of the point A 1 , 2
  4. 4The equation of the plane through the points 2 , - 1,0 , 3 , - 4,5 and parallel to a line with direction cosines proportional to 2,3 and 4 i
  5. 5Let P 1 : x - 2 y + 3 z = 5 and P 2 : 2 x - 3 y + z + 4 = 0 be two planes. The equation of the plane perpendicular to the line of intersecti
  6. 6The perpendicular bisector of a line segment with end points 1,2 , 6 and - 3,6 , 2 passes through - 6,2 , 4 and has the equation of the form
  7. 7If the line x - 1 5 = y - 3 2 = z - 3 2 intersects the curve x 2 - y 2 = k 2 , z = 0 , then the value of 2 k can be equal to
  8. 8The shortest distance between the lines x - 2 2 = y - 3 2 = z - 0 1 and x + 4 - 1 = y - 7 8 = z - 5 4 lies in the interval
  9. 9Let P 1 : 2 x + y + z + 1 = 0 , P 2 : 2 x - y + z + 3 = 0 and P 3 : 2 x + 3 y + z + 5 = 0 be three planes, then the distance of the line of
  10. 10Let L 1 : x = y = z and L 2 : x - 1 = y - 2 = z - 3 be two lines. The foot of perpendicular drawn from the origin O 0,0 , 0 on L 1 to L 2 is
  11. 11Let P 1 : 3 y + z + 1 = 0 and P 2 : 2 x - y + 3 z - 7 = 0 and the equation of line A B is x - 1 2 = y - 3 - 1 = z - 4 3 in 3 D space. Shorte
  12. 12If the planes r → ⋅ i ^ + j ^ + k ^ = 1 , r → ⋅ i ^ + 2 a j ^ + k ^ = 2 and r → ⋅ a i ^ + a 2 j ^ + k ^ = 3 intersect in a line, then the po
  13. 13If the line x - 4 1 = y - 2 1 = z - q p lies completely in the plane 2 x - 4 y + z = 7 , then the ordered pair p , q is
  14. 14Let L be the line through the intersection of the planes 3 x - y + 2 z + 1 = 0 and 3 x - 2 y + z = 3 . Then, the equation of the plane passi
  15. 15A ray of light through the point A 1,2 , 3 strikes the plane x + y + z = 12 at a point B and on reflection passes through the point C 3,5 ,
  16. 16If a x + 13 y + b z + c = 0 is a plane through the line of intersection of 2 x + 3 y - z + 1 = 0 , x + y - 2 z + 3 = 0 and is perpendicular
  17. 17A plane passes through the point - 2 , - 2,2 and contains the line joining the points 1 , - 1,2 and 1,1 , 1 . Then the image of - 7,2 , 3 in
  18. 18The distance of the point 1 , 2 , 3 from the plane x + y - z = 5 measured along the straight line x = y = z is
  19. 19Let A be the point 1 , 2 , 3 and B be a point on the line x - 1 - 2 = y + 1 3 = z - 5 4 = k . The value of k such that line A B is perpendic
  20. 20Distance between two non-intersecting planes P 1 and P 2 is 5 units, where P 1 is 2 x - 3 y + 6 z + 26 = 0 and P 2 is 4 x + b y + c z + d =
  21. 21If the plane a x - b y + c z = d contains the line x - a a = y - 2 d b = z - c c , then the value of b 4 d is equal to b , d 0
  22. 22The projection of the line x - 1 2 = y + 1 1 = z - 2 3 on a plane P is x - 1 1 = y + 1 2 = z - 2 1 , then the equation of the plane P is
  23. 23The length of the perpendicular from 1,0 , 2 on the line x + 1 3 = y - 2 - 2 = z + 1 - 1 is
  24. 24A line parallel to 6 i ^ - 3 j ^ + 2 k ^ intersects the line x 1 = y 2 = z 2 at A and the line x + 1 1 = y + 2 2 = z + 3 2 at B , then the l
  25. 25The shortest distance between the line x = y = z and the line of intersection of 2 x + y + z - 1 = 0 and 3 x + y + 2 z - 2 = 0 is
  26. 26Let L 1 be the projection and L 2 be the image of z -axis in the plane 3 x - 4 y + z + 1 = 0 . The distance of the point 1,2 , 3 from the pl
  27. 27The point of intersection of the plane 3 x - 5 y + 2 z = 6 with the straight line passing through the origin and perpendicular to the plane
  28. 28A plane passes through 1 , - 2 , 1 and is perpendicular to two planes 2 x - 2 y + z = 0 and x - y + 2 z = 4 . The distance of the plane from
  29. 29If the foot of perpendicular drawn from the point 2,5 , 1 on a line passing through α , 2 α , 5 is 1 5 , 2 5 , 3 5 , then α is equal to
  30. 30The direction cosines of two lines satisfy 2 l + 2 m - n = 0 and l m + m n + n l = 0 . The angle between these lines is
  31. 31The image of the line x 2 = y - 1 5 = z + 1 3 in the plane x + y + 2 z = 3 meets the x z - plane at the point a , b , c , then the value of
  32. 32Image of line x - 2 3 = y - 1 1 = z - 1 - 4 in the plane x + y + z = 7 is
  33. 33A line is drawn from the point P 1,1 , 1 and perpendicular to a line whose direction ratios are 1,1 , 1 to intersect the plane x + 2 y + 3 z
  34. 34If the lines x - 3 2 = y - 5 2 = z - 4 and x - 2 = y - 6 4 = z - 5 2 intersect at a point , , , then the greatest value of is equal to
  35. 35Consider the line L : x - 1 2 = y + 1 - 3 = z + 10 8 and a family of planes P containing the line L . The member of the family of planes P w
  36. 36The intercepts made on the x , y and z axes, by the plane which bisects the line joining the points 1,2 , 3 and - 3,4 , 5 at right angles, a
  37. 37Let A → be a vector parallel to the line of intersection of the planes P 1 and P 2 . The plane P 1 is parallel to the vectors 2 j ^ + 3 k ^
  38. 38The length of the perpendicular (in units) from the point 1,2 , 4 on the straight line x - 2 1 = y - 7 2 = z - 3 - 1 lies in the interval
  39. 39Consider the line L x - 1 2 = y + 2 3 = z - 7 6 . Point P 2 , - 5,0 and Q are such that P Q is perpendicular to the line L and the midpoint
  40. 40If the angle between the plane x - 3 y + 2 z = 1 and the line x - 1 2 = y - 1 - 1 = z - 1 - 3 is θ , then sec ⁡ 2 θ is equal to
  41. 41If the image of the point 1 , - 2 , 3 in the plane 2 x + 3 y - z = 7 is the point α , β , γ , then the value of α + β + γ is equal to
  42. 42If the line x - 1 1 = y - k - 2 = z - 3 λ lies in the plane 3 x + 4 y - 2 z = 6, then 5 k + 3 λ is equal to
  43. 43Consider a plane P : 2 x + y - z = 5 , a line L : x - 3 2 = y + 1 - 3 = z - 2 - 1 and a point A 3 , - 4,1 . If the line L intersects plane P
  44. 44Let P 1,2 , 3 be a point in space and Q be a point on the line x - 1 2 = y - 3 5 = z - 1 3 such that P Q is parallel to 5 x - 4 y + 3 z = 1
  45. 45Let P 1 : x + y + 2 z - 4 = 0 and P 2 : 2 x - y + 3 z + 5 = 0 be two planes. Let A 1 , 3 , 4 and B 3 , 2 , 7 be two points in space. The equ
  46. 46The equation of the line which intersect each of the two lines 2 x + y - 1 = 0 = x - 2 y + 3 z and 3 x - y + z + 2 = 0 = 4 x + 5 y - 2 z - 3
  47. 47Lying in the plane x + y + z = 6 is a line L passing through 1,2 , 3 and perpendicular to the line of intersection of planes x + y + z = 6 a
  48. 48If the distance of point P 3,2 , 6 from the line x - 1 2 = y - 2 3 = z - 3 4 measured parallel to the plane 3 x - 5 y + 2 z = 5 is k , then
  49. 49A perpendicular is drawn from a point on the line x - 1 2 = y + 1 - 1 = z 1 to the plane x + y + z = 3 such that the foot of the perpendicul
  50. 50Direction cosines of the normal to the plane containing the lines x 2 = y 3 = z 5 and x - 1 2 = y - 1 3 = z - 1 5 are

Frequently Asked Questions

1.How many questions are available for Three Dimensional Geometry?

This chapter includes 105 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Three Dimensional Geometry chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Three Dimensional Geometry questions in NTA Abhyas (JEE Main)?

Of the 105 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Three Dimensional Geometry should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.