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Mathematics - Three Dimensional Geometry

Practise 55 KCET previous year questions on Three Dimensional Geometry, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KCET tests.

Three Dimensional Geometry has been asked in 15 of the 20 years of KCET papers analysed (2007–2026), with 55 questions in all. 60% of them were easy, 27% moderate and 13% tough. Most of its questions came from 2024, with 5 questions that year. In the last three years (2024–2026) it had 11 questions across 3 papers, about 3.7 per paper.

The chapter's 5 topics are not weighted equally: Line in Space (16 questions, 29%), Plane in Space (14 questions, 25%), and Direction Cosines and Direction Ratios (10 questions, 18%) have been asked the most. Over the last five years the most frequent topics have been Plane in Space (6), Direction Cosines and Direction Ratios (5), and Line in Space (4). Line in Space has produced the most tough questions (4).

  1. 1The angle between the lines whose direction ratios are and is2026Direction Cosines and Direction Ratios
  2. 2The measure of the angle between the lines and is2026Line in Space
  3. 3The three points and form a right-angled triangle with , then the value of "a" is2026Direction Cosines and Direction Ratios
  4. 4If a line makes angles and with and z axes respectively, where is acute, then the value of is2025Direction Cosines and Direction Ratios
  5. 5The equation of the line through the point and perpendicular to the line is2025Line in Space
  6. 6The distance of the point from yz plane is2025Basics of point in 3 dimension
  7. 7If lines and are mutually perpendicular, then is equal to2024Direction Cosines and Direction Ratios
  8. 8The distance between the two planes and is2024Plane in Space
  9. 9The sine of the angle between the straight line are the plane is2024Line and Plane
  10. 10The equation in three-dimensional space represents2024Plane in Space
  11. 11The plane containing the point and the line is2024Line and Plane
  12. 12If a line makes an angle of with each and axis, then the acute angle made by -axis is2023Direction Cosines and Direction Ratios
  13. 13The length of perpendicular drawn from the point to the line is2023Line in Space
  14. 14The equation of the plane through the points and is2023Plane in Space
  15. 15The point of intersection of the line with the plane is2023Line and Plane
  16. 16If is the foot of the perpendicular from to a plane, then the equation of the plane is2023Plane in Space
  17. 17The octant in which the point lies is2022Basics of point in 3 dimension
  18. 18The coordinates of foot of the perpendicular drawn from the origin to the plane are2022Plane in Space
  19. 19The angle between the pair of lines and is2022Line in Space
  20. 20The distance of the point whose position vector is from the plane is2022Plane in Space
  21. 21The equation of the line joining the points and is2021Line in Space
  22. 22The angle between the lines whose direction cosines are and is2021Direction Cosines and Direction Ratios
  23. 23If a plane meets the coordinate axes at and in such a way that the centroid of is at the point , then the equation of the plane is2021Line and Plane
  24. 24The area of the quadrilateral when and is equal to2021Basics of point in 3 dimension
  25. 25The mid points of the sides of triangle are and then centroid of the triangle2021Basics of point in 3 dimension
  26. 26If and are unit vectors and is the angle between and , then is equal to2020Basics of point in 3 dimension
  27. 27If , then is equal to2020Line in Space
  28. 28The point lies in the octant2020Line and Plane
  29. 29If the vectors and are coplanar, then the value of is2020Direction Cosines and Direction Ratios
  30. 30The value of is2020Line in Space
  31. 31Foot of the perpendicular drawn from the point \( (1,3,4) \) to the plane \( 2 x-y+z+3=0 \) is2019Plane in Space
  32. 32Acute angle between the line \( {x-5}{2}= {y+1}{-1}= {z+4}{1} \) and the plane \( 3 x-4 y-z+5=0 \) is2019Line and Plane
  33. 33The distance of the point \( (1,2,1) \) from the line \( {x-1}{2}= {y-2}{1}= {z-3}{2} \) is2019Line in Space
  34. 34\( X Y \) - plane divides the line joining the points \( A(2,3,-5) \) and \( B(-1,-2,-3) \) in the ratio2019Basics of point in 3 dimension
  35. 35A unit vector perpendicular to the plane containing the vectors \( {i}+2 {j}+ {k} \) and \( -2 {i}+ {j}+3 {k} \) is2019Line and Plane
  36. 36The image of the point \( (1,6,3) \) in the line \( {x}{1}= {y-1}{2}= {z-2}{3} \) is2018Line in Space
  37. 37The angle between the lines \( 2 x=3 y=-z \) and \( 6 x=-y=-4 z \) is2018Line in Space
  38. 38The value of \( k \) such that the line \( {x-4}{1}= {y-2}{1}= {z-k}{2} \) lies on the plane \( 2 x-4 y+z=7 \) is2018Line and Plane
  39. 39\( {(x+3) e^{x}}{(x+4)^{2}} d x \) is eqal to2017Plane in Space
  40. 40\( _{- {I}{2}}^{ { }{2}} {d x}{e^{ x}+1} \) is equal to2017Plane in Space
  41. 41If \( {a} \& {b} \) are unit vectors, then the angle between \( {a} \) and \( {b} \) for \( {3} {a}- {b} \) to be unit vector is2017Plane in Space
  42. 42\( 3.5 \) \( _{0.2}[x] d x \) is equal to2017Line in Space
  43. 43The vector equation of the plane which is at a distance of \( {3}{ {14}} \) from the origin and the normal from the origin is \( 2 {i}-3 {j}2016Plane in Space
  44. 44Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane \( 5 y+8 \) \( =0 \) :2016Plane in Space
  45. 45If \( , , \) are the direction cosines of a vector \( {a} \), then \( 2 + 2 + 2 \) is equal to2016Direction Cosines and Direction Ratios
  46. 46If \( f: R R \) is defined by \( f(x)= {x}{x^{2}+1} \) find \( f(f(2)) \)2015Direction Cosines and Direction Ratios
  47. 47Evaluate \( | {array}{cc} 15 & 15 \\ 75 & 75 {array} | \)2015Line in Space
  48. 48A man takes a step forward with probability \( 0.4 \) and one step backward with probability \( 0.6 \), then the probability that at the end2015Plane in Space
  49. 49If \( x+y 2, x 0, y 0 \) the point at which maximum value of \( 3 x+2 y \) attained will be2014Line in Space
  50. 50If \( = \), then2014Plane in Space

Frequently Asked Questions

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

This chapter includes 55 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Three Dimensional Geometry has appeared in 15 of the 20 years of KCET papers covered here, with 55 questions across 15 papers - about 4 per paper it appears in.

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

Of the 55 questions analysed for this chapter, 60% are easy, 27% moderate and 13% tough. 2024 had the most, with 5 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 - 16 questions (29%)
  • Plane in Space - 14 questions (25%)
  • Direction Cosines and Direction Ratios - 10 questions (18%)
  • Line in Space has produced the most tough questions (4).
6.Is Three Dimensional Geometry's weightage in KCET going up or down?

Across all 15 papers analysed, Three Dimensional Geometry has averaged about 3.7 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.