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Mathematics - Three Dimensional Geometry

Practise 352 AP 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 AP EAMCET tests.

Three Dimensional Geometry has been asked in 24 of the 24 years of AP EAMCET papers analysed (2001–2024), with 352 questions in all. 51% of them were easy, 44% moderate and 5% tough. Most of its questions came from 2021, with 40 questions that year. In the last three years (2022–2024) it had 93 questions across 28 papers, about 3.3 per paper.

The chapter's 8 topics are not weighted equally: Plane in Space (103 questions, 29%), Direction Cosines and Direction Ratios (90 questions, 26%), and Basics of point in 3 dimension (66 questions, 19%) have been asked the most. Plane in Space has also led over the last five years, with 53 questions. Direction Cosines and Direction Ratios has produced the most tough questions (5).

  1. 1The circum radius of the triangle formed by the points and is27 May, 2025 (M)Basics of point in 3 dimension
  2. 2Let be the vertices of . If the median through the vertex A is equally inclined to the coordinate axes, then27 May, 2025 (M)Line in Space
  3. 3Equation of the plane passing through the origin and perpendicular to the planes and is27 May, 2025 (M)Plane in Space
  4. 4If the line joining the points and intersects the plane passing through the points and at , then26 May, 2025 (M)Three Dimensional Geometry
  5. 5The vector equation of a plane passing through the line of intersection of the planes and the point is26 May, 2025 (M)Plane in Space
  6. 6The points26 May, 2025 (M)Basics of point in 3 dimension
  7. 7The direction cosines of the line making angles and respectively with and Z axes are26 May, 2025 (M)Direction Cosines and Direction Ratios
  8. 8If the equation of the plane passing through the point and perpendicular to the planes and is , then26 May, 2025 (M)Plane in Space
  9. 9Line passes through the points and . Line passes through the point and is parallel to the vector . If is the point of intersection of the li26 May, 2025 (E)Three Dimensional Geometry
  10. 10The point in the xy-plane which is equidistant from the points and has the coordinates26 May, 2025 (E)Basics of point in 3 dimension
  11. 11If the direction ratios of two lines and are given by and respectively, then the direction ratios of the line which is perpendicular to the 26 May, 2025 (E)Direction Cosines and Direction Ratios
  12. 12If the image of the point with respect to the plane is , then26 May, 2025 (E)Plane in Space
  13. 13In a right angled triangle, if the position vector of the vertex having the right angle is and the position vector of the midpoint of its hy24 May, 2025 (M)Basics of point in 3 dimension
  14. 14Assertion (A) : For the lines and , if , then the two lines are coplanar Reason (R) : is times the shortest distance between the lines and .24 May, 2025 (M)Line in Space
  15. 15The locus of a point at which the line joining the points subtends a right angle, is24 May, 2025 (M)Basics of point in 3 dimension
  16. 16If are the vertices of a triangle ABC, then the direction ratios of the bisector of are24 May, 2025 (M)Direction Cosines and Direction Ratios
  17. 17Let and be four points. If is the acute angle between the plane determined by and the plane determined by , then24 May, 2025 (M)Direction Cosines and Direction Ratios
  18. 18If are the position vectors of four points respectively, then the shortest distance between the lines and is23 May, 2025 (M)Line in Space
  19. 19If and are the vertices of a triangle. If D is the point of intersection of the side BC and the internal angular bisector of angle A, then23 May, 2025 (M)Line in Space
  20. 20A line segment PQ has the length 63 and direction ratios . If this line makes an obtuse angle with X -axis, then the components of the vecto23 May, 2025 (M)Direction Cosines and Direction Ratios
  21. 21A plane given by is perpendicular to the planes and the perpendicular distance from the origin to the plane is units. If all the intercepts 23 May, 2025 (M)Plane in Space
  22. 22If and are the vertices of a triangle, then the distance between its circumcentre and orthocentre is23 May, 2025 (E)Basics of point in 3 dimension
  23. 23If the direction cosines of two lines satisfy the equations , and is the angle between the lines, then23 May, 2025 (E)Direction Cosines and Direction Ratios
  24. 24If is the foot of the perpendicular drawn from the origin to a plane then the equation of that plane is23 May, 2025 (E)Plane in Space
  25. 25is a point on the line parallel to the vector . If is a point on the plane parallel to the vectors and , then the point of intersection of t22 May, 2025 (M)Line and Plane
  26. 26If are the vertices of a triangle ABC, then the -coordinate of its incentre is22 May, 2025 (M)Basics of point in 3 dimension
  27. 27A plane is passing through the points and . If the plane is perpendicular the plane , then the perpendicular distance from to the plane is22 May, 2025 (M)Plane in Space
  28. 28The points in the Argand plane represented by the complex numbers , and form22 May, 2025 (E)Basics of point in 3 dimension
  29. 29For a positive real number , if the perpendicular distance from a point to the plane is 6 units, then22 May, 2025 (E)Plane in Space
  30. 30If is the harmonic conjugate of the point with respect to the line segment joining the points and , then22 May, 2025 (E)Basics of point in 3 dimension
  31. 31On a line with direction cosines is a fixed point. If and then the ratio in which the point B divides the line segment joining A and C is22 May, 2025 (E)Basics of point in 3 dimension
  32. 32If the line of intersection of the planes and makes an angle with the positive x -axis, then22 May, 2025 (E)Line in Space
  33. 33is the centroid of the triangle ABC. If and then21 May, 2025 (M)Basics of point in 3 dimension
  34. 34If the sum of the distances of the point from X -axis, Y -axis and Z-axis is minimum, then21 May, 2025 (M)Basics of point in 3 dimension
  35. 35If the equation of the plane passing through the point and perpendicular to each of the planes and is , then21 May, 2025 (M)Plane in Space
  36. 36The point of intersection of the lines represented by and is21 May, 2025 (E)Line in Space
  37. 37If and are the vertices of a tetrahedron, then the acute angle between its face and edge is21 May, 2025 (E)Line and Plane
  38. 38If the four points and are coplanar, then21 May, 2025 (E)Algebra of Vectors
  39. 39If the direction cosines of two lines are given by and , then the acute angle between those lines is23 May, 2024 (M)Direction Cosines and Direction Ratios
  40. 40If the angle between the line and the plane in such that , then the value of23 May, 2024 (M)Line and Plane
  41. 41The distance of a point from the plane is22 May, 2024 (M)Plane in Space
  42. 42The orthocentre of triangle formed by points: , and is22 May, 2024 (M)Basics of point in 3 dimension
  43. 43If the perpendicular distance from to the plane is 3 , then22 May, 2024 (M)Line in Space
  44. 44If and are three points then the ratio in which the point C divides AB externally is22 May, 2024 (E)Basics of point in 3 dimension
  45. 45The values of for which the angle between the vectors and is obtuse, lie in the interval22 May, 2024 (E)Direction Cosines and Direction Ratios
  46. 46If a line L makes angles and with Y -axis and Z -axis respectively, then the angle between L and another line having direction ratios is22 May, 2024 (E)Direction Cosines and Direction Ratios
  47. 47If are the direction cosines of a line that is perpendicular to the lines having the direction ratios and then22 May, 2024 (E)Direction Cosines and Direction Ratios
  48. 48The foot of the perpendicular drawn from a point A on to a plane is . If the equation of the plane parallel to the plane and passing through22 May, 2024 (E)Plane in Space
  49. 49If lies on the plane an lies on the plane then 1 direction cosines of the line PQ are21 May, 2024 (M)Direction Cosines and Direction Ratios
  50. 50Let be the plane that passes through the point and parallel to the plane . Then the foot of perpendicular drawn from the point to the plane 21 May, 2024 (M)Plane in Space

Frequently Asked Questions

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

This chapter includes 352 questions compiled from AP EAMCET papers spanning 2001 to 2025.

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

These are AP 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 AP EAMCET Mathematics?

Three Dimensional Geometry has appeared in 25 of the 25 years of AP EAMCET papers covered here, with 352 questions across 93 papers - about 4 per paper it appears in.

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

Of the 352 questions analysed for this chapter, 51% are easy, 44% moderate and 5% tough. 2021 had the most, with 40 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 - 103 questions (29%)
  • Direction Cosines and Direction Ratios - 90 questions (26%)
  • Basics of point in 3 dimension - 66 questions (19%)
  • Direction Cosines and Direction Ratios has produced the most tough questions (5).
6.Is Three Dimensional Geometry's weightage in AP EAMCET going up or down?

Across all 93 papers analysed, Three Dimensional Geometry has averaged about 3.8 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 3.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.