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Mathematics - Three Dimensional Geometry

Practise 276 TS EAMCET previous year questions on Three Dimensional Geometry, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty TS EAMCET tests.

Three Dimensional Geometry has been asked in 24 of the 24 years of TS EAMCET papers analysed (2001–2024), with 276 questions in all. 50% of them were easy, 45% moderate and 5% tough. Most of its questions came from 2020, with 37 questions that year. In the last three years (2022–2024) it had 68 questions across 17 papers, about 4 per paper.

The chapter's 6 topics are not weighted equally: Plane in Space (90 questions, 33%), Direction Cosines and Direction Ratios (64 questions, 23%), and Basics of point in 3 dimension (52 questions, 19%) have been asked the most. Plane in Space has also led over the last five years, with 41 questions. Plane in Space has produced the most tough questions (6).

  1. 1ABCD is a tetrahedron. are the position vectors of the points respectively. is the position vector of the centroid of the triangular face BC04 May, 2025 (M)Basics of point in 3 dimension
  2. 2The equation of the locus of a point whose distance from XY-plane is twice its distance from Z -axis is04 May, 2025 (M)Basics of point in 3 dimension
  3. 3If is the angle between any two diagonals of a cube and is the angle between a diagonal of a cube and a diagonal of its face, which intersec04 May, 2025 (M)Direction Cosines and Direction Ratios
  4. 4If the angle between the planes and is then the direction ratios of the line perpendicular to the plane are04 May, 2025 (M)Direction Cosines and Direction Ratios
  5. 5A plane contains the vectors and . Another plane contains the vectors and is a vector parallel to the line of intersection of and . If the a04 May, 2025 (E)Line in Space
  6. 6Consider the following Assertion (A): The two lines and intersect each other. Reason (R): The shortest distance between the lines and is equ04 May, 2025 (E)Line in Space
  7. 7Let and be two points in space. If YZ plane and ZX plane respectively divide the line segment joining the points A and B in the ratio and 4:04 May, 2025 (E)Basics of point in 3 dimension
  8. 8The direction ratios of the line bisecting the angle between the -axis and the line having direction ratios are04 May, 2025 (E)Direction Cosines and Direction Ratios
  9. 9If the plane is at a distance of two units from the plane , then the product of all the possible values of is04 May, 2025 (E)Plane in Space
  10. 10Let be the plane determined by the vectors and be the plane determined by the vectors . Let be a non-zero vector parallel to the line of int03 May, 2025 (M)Direction Cosines and Direction Ratios
  11. 11If is the ratio in which the point divides the line segment joining the points and where p is an integer then03 May, 2025 (M)Basics of point in 3 dimension
  12. 12If is the foot of the perpendicular drawn from a point to the line joining the points and , then03 May, 2025 (M)Line in Space
  13. 13If are the vertices of a triangle ABC and the equation of the plane containing the triangle ABC is , then03 May, 2025 (M)Plane in Space
  14. 14The number of values of ' ' for which the points form a right-angled isosceles triangle is03 May, 2025 (E)Basics of point in 3 dimension
  15. 15A line makes angles with positive -axes respectively. If is an acute angle, then03 May, 2025 (E)Direction Cosines and Direction Ratios
  16. 16If the foot of the perpendicular drawn from the point to the plane is and the equation of the plane is then03 May, 2025 (E)Plane in Space
  17. 17The point of intersection of the line joining the points and the plane passing through the points is02 May, 2025 (M)Line and Plane
  18. 18The shortest distance between the lines and is02 May, 2025 (M)Line in Space
  19. 19If are the vertices of a triangle ABC and the bisector of angle A meets the side BC at D, then02 May, 2025 (M)Line in Space
  20. 20If the direction cosines of two lines satisfy the equations , and is the angle between the lines then02 May, 2025 (M)Direction Cosines and Direction Ratios
  21. 21If the equation of the plane passing through the points and perpendicular to the plane is then02 May, 2025 (M)Plane in Space
  22. 22Let A be a point having position vector and be a line. If P is a point on this line and is at a minimum distance from the plane , then the e02 May, 2025 (E)Line and Plane
  23. 23and are the vertices of a tetrahedron. If G is the centroid of the tetrahedron and is the centroid of its face ABC, then the point which div02 May, 2025 (E)Basics of point in 3 dimension
  24. 24If L is a line common to the planes then the direction ratios of the line L are02 May, 2025 (E)Direction Cosines and Direction Ratios
  25. 25If the points and are equidistant from the plane , then the values of are02 May, 2025 (E)Plane in Space
  26. 26A plane passing through the points is parallel to the vector , If a line joining the points and intersects the plane at the point , then11 May, 2024 (M)Plane in Space
  27. 27A unit vector is coplanar with the vectors and . If is perpendicular to the vector then11 May, 2024 (M)Line in Space
  28. 28and are two planes. A plane passing through the line of intersection of these two planes, passes through the point . If the equation of is ,11 May, 2024 (M)Plane in Space
  29. 29The foot of the perpendicular drawn from the point to a plane is . If are the intercepts made by the plane on -axes respectively, then11 May, 2024 (M)Line and Plane
  30. 30and are the points of trisection of the line segment . If and are the position vectors of and respectively, then the position vector of the 10 May, 2024 (M)Basics of point in 3 dimension
  31. 31The position vector of the point of intersection of the line joining the points and the line joining the points is10 May, 2024 (M)Line in Space
  32. 32A plane passing through the point is perpendicular to the vector and another plane passing through the point is perpendicular to the vector 10 May, 2024 (M)Plane in Space
  33. 33are the vertices of . If and , then is10 May, 2024 (M)Basics of point in 3 dimension
  34. 34If are the intercepts made on -axes respectively by the plane passing through the points and , then10 May, 2024 (M)Plane in Space
  35. 35is a unit vector normal to the plane containing the vectors and . If this plane passes through the point and p is the perpendicular distance10 May, 2024 (E)Plane in Space
  36. 36If are position vectors of two points and are two vectors, then the lines are10 May, 2024 (E)Line in Space
  37. 37If the harmonic conjugate of with respect to the line segment joining the points and is , then10 May, 2024 (E)Basics of point in 3 dimension
  38. 38If is the line of intersection of two planes and and the direction ratios of the line are , then10 May, 2024 (E)Plane in Space
  39. 39The foot of the perpendicular drawn from onto the plane is . If is a plane then10 May, 2024 (E)Line in Space
  40. 40If are non-coplanar vector and the points are coplanar, then one of the values of is09 May, 2024 (M)Direction Cosines and Direction Ratios
  41. 41If the ratio of the perpendicular distances of a variable point from the -axis and from the -plane in , then the equation of the locus of is09 May, 2024 (M)Plane in Space
  42. 42The direction cosines of two lines are connected by the relation and . If is the angle between these two lines, then09 May, 2024 (M)Direction Cosines and Direction Ratios
  43. 43A plane passes through the points and . If is the perpendicular distance from the origin to the plane and are the direction cosin of a norma09 May, 2024 (M)Plane in Space
  44. 44and are the direction ratios of two lines and is the angle between them. If , then09 May, 2024 (E)Direction Cosines and Direction Ratios
  45. 45A plane ( ) passing through the point is perpendicular to the planes and . If the equation of the plane is then09 May, 2024 (E)Plane in Space
  46. 46In a triangle , if the mid points of sides , CA are respectively, then14 May, 2023 (M)Basics of point in 3 dimension
  47. 47If and are direction cosines of two lines then14 May, 2023 (M)Direction Cosines and Direction Ratios
  48. 48If is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is14 May, 2023 (M)Line and Plane
  49. 49If the circumcenter of the triangle formed by the points and is , then14 May, 2023 (E)Basics of point in 3 dimension
  50. 50If is the acute angle between the two lines whose direction cosines are connected by the relations and , then14 May, 2023 (E)Line in Space

Frequently Asked Questions

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

This chapter includes 276 questions compiled from TS EAMCET papers spanning 2001 to 2025.

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

These are TS EAMCET 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 TS EAMCET Mathematics?

Three Dimensional Geometry has appeared in 25 of the 25 years of TS EAMCET papers covered here, with 276 questions across 64 papers - about 4 per paper it appears in.

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

Of the 276 questions analysed for this chapter, 50% are easy, 45% moderate and 5% tough. 2020 had the most, with 37 questions.

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

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

  • Plane in Space - 90 questions (33%)
  • Direction Cosines and Direction Ratios - 64 questions (23%)
  • Basics of point in 3 dimension - 52 questions (19%)
  • Plane in Space has produced the most tough questions (6).
6.Is Three Dimensional Geometry's weightage in TS EAMCET going up or down?

Across all 64 papers analysed, Three Dimensional Geometry has averaged about 4.3 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 4.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.