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Mathematics - Three Dimensional Geometry

Practise 37 Manipal (MET) previous year questions on Three Dimensional Geometry, compiled from papers spanning 2010 to 2023. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty Manipal (MET) tests.

Three Dimensional Geometry has been asked in 12 of the 15 years of Manipal (MET) papers analysed (2010–2024), with 37 questions in all. 57% of them were easy, 35% moderate and 8% tough. Most of its questions came from 2016, with 6 questions that year. In the last three years (2022–2024) it had 4 questions across 2 papers, about 2 per paper.

The chapter's 5 topics are not weighted equally: Plane in Space (13 questions, 35%), Direction Cosines and Direction Ratios (11 questions, 30%), and Line and Plane (6 questions, 16%) have been asked the most. Over the last five years the most frequent topics have been Line in Space (3), Direction Cosines and Direction Ratios (1), and Line and Plane (1). Direction Cosines and Direction Ratios has produced the most tough questions (1).

  1. 1If the line and intersect, then is equal to2023Line in Space
  2. 2If the foot of the perpendicular drawn from the point on a line passing through is , then is equal to_____2023Line in Space
  3. 3If the lines and are coplanar, then can have2022Line and Plane
  4. 4If the foot of the perpendicular drawn from the point on a line passing through is , then is equal to _____2022Line in Space
  5. 5If are the angles which a half ray makes with the positive direction of the axes, then is equal to2021Direction Cosines and Direction Ratios
  6. 6Equation of a plane passing through and and perpendicular to is2020Plane in Space
  7. 7If , then the projection of on is2019Direction Cosines and Direction Ratios
  8. 8If a line makes with the positive direction of and -axes respectively. Then, is equal to2019Direction Cosines and Direction Ratios
  9. 9The projection of a line on a co-ordinate axes are . Then the length of the line is2019Direction Cosines and Direction Ratios
  10. 10A perpendicular is drawn from the point to the line . The equation of the perpendicular from to the given line is2019Line in Space
  11. 11The direction cosines of any normal to the -plane are2019Direction Cosines and Direction Ratios
  12. 12If are the direction cosines of a line, then the value of is2018Direction Cosines and Direction Ratios
  13. 13If are the position vectors of respectively such that , then divides in the ratio2018Basics of point in 3 dimension
  14. 14If are the angles which a half ray makes with the positive direction of the axes, then is equal to2017Direction Cosines and Direction Ratios
  15. 15The volume of the parallelopiped whose sides are given by ,2017Direction Cosines and Direction Ratios
  16. 16The direction cosines of two lines are connected by the relations , then the angle between them is2016Direction Cosines and Direction Ratios
  17. 17The equation of the plane through the points and parallel to -axis is2016Plane in Space
  18. 18If is the image of the point under the reflection in the plane , then the equation of the line is2016Plane in Space
  19. 19The equation of the plane passing through the line of intersection of the planes and and perpendicular to the plane is2016Line and Plane
  20. 20A vector perpendicular to the plane containing the points , is2016Plane in Space
  21. 21The vector equation of the plane through the point and perpendicular to the line of intersection of the plane and is2016Direction Cosines and Direction Ratios
  22. 22The image of the point in the plane , is2015Plane in Space
  23. 23Equation of the plane that contains the lines and , is2015Plane in Space
  24. 24The distance of the point from the line measured parallel to the plane , is2015Line and Plane
  25. 25The equation of the plane through the intersection of the planes and and parallel to -axis, is2015Plane in Space
  26. 26The line joining the points and meets the plane at the point2014Line and Plane
  27. 27The distance of the point , from the plane measured along the line is2014Line and Plane
  28. 28The image of the point with position vector in the plane is2014Plane in Space
  29. 29The equation of the plane through the intersection of the planes and and the point is2014Plane in Space
  30. 30The equations of the lines passing through the point and at a distance from the origin are2014Line in Space
  31. 31The image of the point with position vector in the plane is2011Plane in Space
  32. 32The equation of plane passing through a point and parallel to the vectors and is2011Plane in Space
  33. 33If and be four points such that , then the lines and are2010Line in Space
  34. 34The direction cosines of any normal to the -plane are2010Direction Cosines and Direction Ratios
  35. 35The locus of the equation is2010Plane in Space
  36. 36The reflection of the point in the plane is2010Plane in Space
  37. 37Radius of the circle2010Line and Plane

Frequently Asked Questions

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

This chapter includes 37 questions compiled from Manipal (MET) papers spanning 2010 to 2023.

2.Are these questions only from Manipal (MET), or from other exams too?

These are Manipal (MET) 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 Manipal (MET) Mathematics?

Three Dimensional Geometry has appeared in 12 of the 15 years of Manipal (MET) papers covered here, with 37 questions across 12 papers - about 3 per paper it appears in.

4.What is the difficulty level of Three Dimensional Geometry questions in Manipal (MET)?

Of the 37 questions analysed for this chapter, 57% are easy, 35% moderate and 8% tough. 2016 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:

  • Plane in Space - 13 questions (35%)
  • Direction Cosines and Direction Ratios - 11 questions (30%)
  • Line and Plane - 6 questions (16%)
  • Direction Cosines and Direction Ratios has produced the most tough questions (1).
6.Is Three Dimensional Geometry's weightage in Manipal (MET) going up or down?

Across all 12 papers analysed, Three Dimensional Geometry has averaged about 3.1 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.