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Mathematics - Three Dimensional Geometry

Practise 45 VITEEE previous year questions on Three Dimensional Geometry, compiled from papers spanning 2006 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty VITEEE tests.

Three Dimensional Geometry has been asked in 18 of the 18 years of VITEEE papers analysed (2006–2024), with 45 questions in all. 40% of them were easy, 42% moderate and 18% tough. Most of its questions came from 2015, with 6 questions that year. In the last three years (2022–2024) it had 6 questions across 3 papers, about 2 per paper.

The chapter's 5 topics are not weighted equally: Line in Space (23 questions, 51%), Line and Plane (9 questions, 20%), and Plane in Space (8 questions, 18%) have been asked the most. Over the last five years the most frequent topics have been Line and Plane (4), Line in Space (3), and Plane in Space (2). Line and Plane has produced the most tough questions (4).

  1. 1If the distance between the planes and can be expressed as , then the value of is2024Plane in Space
  2. 2The value of ' ' for which the lines and intersect, is2024Line in Space
  3. 3The equation of the right bisector plane of the segment joining \((2,3,4)\) and \((6,7,8)\) is2023Plane in Space
  4. 4What is the angle between the line \(6 x=4 y=3 z\) and the plane \(3 x+2 y-3 z=4\) ?2023Line and Plane
  5. 5A sphere of constant radius \(2 {k}\) passes through the origin and meets the axes in A, B, C. The locus of the centroid of the tetrahedron 2022Line and Plane
  6. 6The equation of the line passing through \((1,2,3)\) and parallel to the planes \(r ( {i}- {j}+2 {k})=5\) and r. \((3 {i}+ {j}+ {k})=6\) is2022Line and Plane
  7. 7The shortest distance between the lines and is2021Line in Space
  8. 8If the angle between the line and the plane is such that then the value of is2021Line and Plane
  9. 9The distance of the point from the point of intersection of the line and the plane is2021Line in Space
  10. 10If vector equation of the line , is then is equal to2019Line in Space
  11. 11The equation of the plane which bisects the angle between the planes and which contains the origin is2019Plane in Space
  12. 12The vector equation of the symmetrical form of equation of straight line is2018Line in Space
  13. 13Let the line lie in the plane . Then equals2018Line and Plane
  14. 14The radius of the sphere is2018Basics of point in 3 dimension
  15. 15The line which passes through the origin and intersect the two lines , is2017Line in Space
  16. 16The distance of the point from the plane measured parallel to the line is2017Plane in Space
  17. 17Atetrahedron has vertices at and . Then the angle between the faces and will be2016Line in Space
  18. 18A variable plane remains at constant distance , from the origin.If it meets coordinate axes at points then the locus of the centroid of is2016Plane in Space
  19. 19The shortest distance between the lines and is2016Line in Space
  20. 20If is one end of a diameter of the sphere , then the coordinates of the other end of the diameter are2015Plane in Space
  21. 21The two lines and , are perpendicular to each other, if2015Line in Space
  22. 22A tetrahedron has vertices at , and . Then, the angle between the faces and will be2015Line in Space
  23. 23If a line segment makes angles of and with -axis and -axis, respectively. Then, the direction cosines are2015Direction Cosines and Direction Ratios
  24. 24The shortest distance between the lines and is2015Line in Space
  25. 25If a plane passing through the point and is perpendicular to the planes and . Then, the equation of the plane is2015Plane in Space
  26. 26If the points and lie on the opposite sides of the plane , then2014Line in Space
  27. 27Two lines and intersect at a point, if is equal to2014Line in Space
  28. 28If a plane meets the coordinate axes at and such that the centroid of the triangle is , then the equation of the plane is2014Line and Plane
  29. 29is a fixed point on a line through the origin equally inclined to the axes, then anyplane through perpendicular to , makes intercepts on the2013Line in Space
  30. 30If a plane meets the coordinate axes at and in such a way that the centroid of is at the point , then equation of the plane is2012Plane in Space
  31. 31A line making angles and with the positive directions of the axes of and makes with the positive direction of -axis, an angle of2011Direction Cosines and Direction Ratios
  32. 32If , then arg is2010Line and Plane
  33. 33Domain of the function , is2010Line in Space
  34. 34The angle between the lines whose direction cosines satisfy the equations , is2009Line in Space
  35. 35If and are respectively the magnitudes of the vectors then the correct order of and is2009Direction Cosines and Direction Ratios
  36. 36The perimeter of the triangle with vertices at and is2009Line in Space
  37. 37The radius of the sphere is2009Line in Space
  38. 38The shortest distance between the straight lines through the points and , in the directions of and is2008Line and Plane
  39. 39Solution of the differential equation is2008Line in Space
  40. 40Probability of getting positive integral roots of the equation for the integer is2008Line in Space
  41. 41The length of the straight line intercepted by the hyperbola is2007Line in Space
  42. 42The curve described parametrically by represents2007Direction Cosines and Direction Ratios
  43. 43The general solution of the differential equation is given by2007Line in Space
  44. 44The number of positive integral solutions of the equation is2007Line in Space
  45. 45The solution of is2006Line and Plane

Frequently Asked Questions

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

This chapter includes 45 questions compiled from VITEEE papers spanning 2006 to 2024.

2.Are these questions only from VITEEE, or from other exams too?

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

3.Is Three Dimensional Geometry an important chapter for VITEEE Mathematics?

Three Dimensional Geometry has appeared in 18 of the 18 years of VITEEE papers covered here, with 45 questions across 18 papers - about 3 per paper it appears in.

4.What is the difficulty level of Three Dimensional Geometry questions in VITEEE?

Of the 45 questions analysed for this chapter, 40% are easy, 42% moderate and 18% tough. 2015 had the most, with 6 questions.

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

These topics have carried the most weightage in Three Dimensional Geometry:

  • Line in Space - 23 questions (51%)
  • Line and Plane - 9 questions (20%)
  • Plane in Space - 8 questions (18%)
  • Line and Plane has produced the most tough questions (4).
6.Is Three Dimensional Geometry's weightage in VITEEE going up or down?

Across all 18 papers analysed, Three Dimensional Geometry has averaged about 2.5 questions per paper. In the last three years (2022–2024), that average has fallen, at about 2.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.