Jump to a section

Mathematics - Vector Algebra

Practise 306 JEE Main previous year questions on Vector Algebra, compiled from papers spanning 2002 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 JEE Main tests.

Vector Algebra has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 306 questions in all. 36% of them were easy, 51% moderate and 13% tough. Most of its questions came from 2023, with 48 questions that year. In the last three years (2024–2026) it had 68 questions across 49 papers, about 1.4 per paper.

The chapter's 4 topics are not weighted equally: Product of 2 vectors (186 questions, 61%), Algebra of Vectors (79 questions, 26%), and Vector Triple Product (21 questions, 7%) have been asked the most. Product of 2 vectors has also led over the last five years, with 102 questions. Product of 2 vectors has produced the most tough questions (23).

  1. 1Let , and a vector be such that . If , then is equal to:08 Apr, 2026 (E)Product of 2 vectors
  2. 2If , and be three vectors such that and , then is equal to _______.06 Apr, 2026 (M)Product of 2 vectors
  3. 3Let and . Then the square of the area of the triangle with adjacent sides determined by the vectors and is :06 Apr, 2026 (E)Product of 2 vectors
  4. 4Let and . If is a vector such that and , then is equal to:05 Apr, 2026 (M)Algebra of Vectors
  5. 5Let be the origin, and . If is the point on such that , and is the point such that , then is equal to :05 Apr, 2026 (E)Algebra of Vectors
  6. 6Let and , where , for some , . Then the value of is _____.04 Apr, 2026 (M)Product of 2 vectors
  7. 7Let and be unit vectors inclined at an acute angle such that . If , then is equal to:04 Apr, 2026 (E)Product of 2 vectors
  8. 8If and are two vectors such that and , then the maximum value of is :02 Apr, 2026 (M)Algebra of Vectors
  9. 9Let the vectors and . For some , let . If and , then is equal to:02 Apr, 2026 (E)Algebra of Vectors
  10. 10Two adjacent sides of a parallelogram PQRS are given by and . If the side PS is rotated about the point P by an acute angle in the plane of 02 Apr, 2026 (E)Product of 2 vectors
  11. 11For three unit vectors satisfying and , the positive value of k is28 Jan, 2026 (M)Product of 2 vectors
  12. 12Let be a triangle such that and . Let S be the point on QR, which is equidistant from the lines PQ and PR. If and , then the value of is28 Jan, 2026 (M)Algebra of Vectors
  13. 13Let be a point in the plane of the vectors and such that is equidistant from the lines AB and AC. If , then the area of the triangle ABP is:28 Jan, 2026 (E)Product of 2 vectors
  14. 14Let and . Let be a vector such that and the angle between and is . Then is equal to24 Jan, 2026 (M)Product of 2 vectors
  15. 15Let and . If is a vector such that and , then is equal to24 Jan, 2026 (E)Product of 2 vectors
  16. 16Let and . Let be the vector in the plane of the vectors and , such that the length of its projection on the vector is . Then is equal to24 Jan, 2026 (E)Algebra of Vectors
  17. 17Let and . Then is equal to :23 Jan, 2026 (M)Product of 2 vectors
  18. 18Let and . If and the length of the projection of on is , then is equal to23 Jan, 2026 (E)Product of 2 vectors
  19. 19Let be three vectors such that . If , and the angle between and is , then is equal to23 Jan, 2026 (E)Product of 2 vectors
  20. 20Let and . Let the projection of the vector on the diagonal of the parallelogram ABCD be of length one unit. If , where , be the roots of the22 Jan, 2026 (M)Product of 2 vectors
  21. 21Let and be two vectors. Let and be a vector of magnitude 2 in -plane. If , then the maximum possible value of is equal to :22 Jan, 2026 (E)Product of 2 vectors
  22. 22Let a vector , make an obtuse angle with the vector and an angle , with the positive -axis. If the set of all possible values of is , then i22 Jan, 2026 (E)Product of 2 vectors
  23. 23Let and be vector such that . If , then is equal to :21 Jan, 2026 (M)Product of 2 vectors
  24. 24For a triangle ABC, let and . If and , where is the angle between and , then is equal to :21 Jan, 2026 (E)Product of 2 vectors
  25. 25Let and . Let be a unit vector in the plane of the vectors and and be perpendicular to . Then such a vector is :08 Apr, 2025 (E)Product of 2 vectors
  26. 26Let the angle between two unit vectors and be . If the vector then the value of is07 Apr, 2025 (M)Product of 2 vectors
  27. 27Let and be the vectors of the same magnitude such that . Then is :07 Apr, 2025 (E)Algebra of Vectors
  28. 28Consider two vectors and . The angle between them is given by . Let , where is parallel to and is perpendicular to . Then the value is equal04 Apr, 2025 (M)Product of 2 vectors
  29. 29Let the three sides of a triangle be given by the vectors and . Let be the centroid of the triangle . Then is equal to ________04 Apr, 2025 (E)Algebra of Vectors
  30. 30Let and be a unit vector such that and , If is perpendicular to , then is equal to _______ .03 Apr, 2025 (M)Product of 2 vectors
  31. 31Let , and be a vector such that and . Then is equal to ______ .03 Apr, 2025 (E)Product of 2 vectors
  32. 32Let be a tetrahedron such that the edges and AD are mutually perpendicular. Let the areas of the triangles and ADB be 5,6 and 7 square units02 Apr, 2025 (M)Product of 2 vectors
  33. 33If is nonzero vector such that its projections on the vectors and are equal, then a unit vector along is:02 Apr, 2025 (M)Product of 2 vectors
  34. 34Let and a vector be such that and . If , then is equal to :02 Apr, 2025 (E)Product of 2 vectors
  35. 35Let \( { {a}}=2 {i}- {j}+3 {k}, { {~b}}=3 {i}-5 {j}+ {k}\) and \( { {c}}\) be a vector such that \( { {a}} { {c}}= { {c}} { {b}}\) and \(( {29 Jan, 2025 (M)Product of 2 vectors
  36. 36Let be a unit vector perpendicular to the vectors and , and makes an angle of with the vector . If makes an angle of with the vector , then 29 Jan, 2025 (E)Product of 2 vectors
  37. 37Let and . If is a vector such that , and the angle between and is , then is equal to28 Jan, 2025 (M)Product of 2 vectors
  38. 38If the components of along and perpendicular to respectively, are and , then is equal to :28 Jan, 2025 (E)Product of 2 vectors
  39. 39Let A, B, C be three points in -plane, whose position vector are given by and respectively with respect to the origin O . If the distance of28 Jan, 2025 (E)Algebra of Vectors
  40. 40Let and be three vectors such that is coplanar with and . If the vector is perpendicular to and , then is equal to24 Jan, 2025 (M)Algebra of Vectors
  41. 41Let the position vectors of three vertices of a triangle be and . If the position vectors of the orthocenter and the circumcenter of the tri24 Jan, 2025 (E)Product of 2 vectors
  42. 42Let and . Then the projection of on is :24 Jan, 2025 (E)Product of 2 vectors
  43. 43Let the position vectors of the vertices and of a tetrahedron be and respectively. The altitude from the vertex to the opposite face meets t23 Jan, 2025 (M)Algebra of Vectors
  44. 44Let be the projection vector of , on the vector . If , then the area of the parallelogram formed by the vectors and is ________22 Jan, 2025 (M)Product of 2 vectors
  45. 45Let and be two unit vectors such that the angle between them is . If and are perpendicular to each other, then the number of values of in is22 Jan, 2025 (E)Algebra of Vectors
  46. 46Let three vectors form a triangle such that and the area of the triangle is . If is a positive real number, then is equal to:09 Apr, 2024 (M)Product of 2 vectors
  47. 47Let and , where is the origin. If the area of the parallelogram with adjacent sides and is 15 sq. units, then the area (in sq. units) of the09 Apr, 2024 (M)Product of 2 vectors
  48. 48Between the following two statements: Statement I : Let and . Then the vector satisfying and is of magnitude . Statement II : In a triangle 09 Apr, 2024 (E)Product of 2 vectors
  49. 49Let , where and are integers and . Let the values of the ordered pair , for which the area of the parallelogram of diagonals and is , be and09 Apr, 2024 (E)Product of 2 vectors
  50. 50The set of all , for which the vectors and are inclined at an obtuse angle for all , is08 Apr, 2024 (M)Product of 2 vectors

Frequently Asked Questions

1.How many questions are available for Vector Algebra?

This chapter includes 306 questions compiled from JEE Main papers spanning 2002 to 2026.

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

These are JEE Main questions specifically for the Vector Algebra chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Vector Algebra an important chapter for JEE Main Mathematics?

Vector Algebra has appeared in 25 of the 25 years of JEE Main papers covered here, with 306 questions across 195 papers - about 2 per paper it appears in.

4.What is the difficulty level of Vector Algebra questions in JEE Main?

Of the 306 questions analysed for this chapter, 36% are easy, 51% moderate and 13% tough. 2023 had the most, with 48 questions.

5.Which topics in Vector Algebra should I focus on?

These topics have carried the most weightage in Vector Algebra:

  • Product of 2 vectors - 186 questions (61%)
  • Algebra of Vectors - 79 questions (26%)
  • Vector Triple Product - 21 questions (7%)
  • Product of 2 vectors has produced the most tough questions (23).
6.Is Vector Algebra's weightage in JEE Main going up or down?

Across all 195 papers analysed, Vector Algebra has averaged about 1.6 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.