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Mathematics - Vector Algebra

Practise 46 JEE Advanced previous year questions on Vector Algebra, compiled from papers spanning 2006 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 Advanced tests.

Vector Algebra has been asked in 21 of the 27 years of JEE Advanced papers analysed (2000–2026), with 46 questions in all. 26% of them were easy, 54% moderate and 20% tough. Most of its questions came from 2010, with 4 questions that year. In the last three years (2024–2026) it had 6 questions across 6 papers, about 1 per paper.

The chapter's 4 topics are not weighted equally: Product of 2 vectors (18 questions, 39%), Algebra of Vectors (15 questions, 33%), and Scalar Triple Product (9 questions, 20%) have been asked the most. Product of 2 vectors has also led over the last five years, with 5 questions. Scalar Triple Product has produced the most tough questions (3).

  1. 1Let be two vectors, and let and be the points with position vectors , and , respectively, with respect to the origin . If , , and and are pe2026 (Paper 2)Product of 2 vectors
  2. 2For any two points and in the -plane, let denote the vector from to , and denote the zero vector. Let and be three distinct points in the -p2025 (Paper 1)Algebra of Vectors
  3. 3Let , and and be two vectors such that and . Let and be real numbers such that , and . Match each entry in List-I to the correct entry in Li2025 (Paper 1)Product of 2 vectors
  4. 4Consider the vectors For two distinct positive real numbers and , define If the vectors , and lie in a plane, the value of is ______ .2025 (Paper 2)Scalar Triple Product
  5. 5Let and be three vectors, where and denotes the origin. If and the point lies on the plane , then the value of is ____2024 (Paper 1)Product of 2 vectors
  6. 6Let and . If for some real numbers , and , we have then the value of is2024 (Paper 2)Product of 2 vectors
  7. 7Let P be the plane 3 x + 2 y + 3 z = 16 and let S = i ^ + j ^ + k ^ : 2 + 2 + 2 = 1 and the distance of , , from the plane P is 7 2 } . Let 2023 (Paper 1)Scalar Triple Product
  8. 8Let the position vectors of points P , Q , R and S be a = i ^ + 2 j ^ - 5 k ^ , b = 3 i ^ + 6 j ^ + 3 k ^ , c = 17 5 i ^ + 16 5 j ^ + 7 k ^ 2023 (Paper 2)Algebra of Vectors
  9. 9Let i ^ , j ^ and k ^ be the unit vectors along the three positive coordinate axes. Let a = 3 i ^ + j ^ - k ^ b = i ^ + b 2 j ^ + b 3 k ^ , 2022 (Paper 2)Product of 2 vectors
  10. 10Let u , v and w be vectors in three-dimensional space, where u and v are unit vectors which are not perpendicular to each other and u w = 1 2021 (Paper 1)Scalar Triple Product
  11. 11Let O be the origin and O A = 2 i ^ + 2 j ^ + k ^ , O B = i ^ - 2 j ^ + 2 k ^ and O C = 1 2 O B - O A for some 0 . If O B O C = 9 2 , then w2021 (Paper 2)Product of 2 vectors
  12. 12In a triangle P Q R , let a = Q R , b = R P and c = P Q . If a = 3 , b = 4 and a . c b c . a b = a a + b , then the value of a b 2 is ______2020 (Paper 1)Product of 2 vectors
  13. 13Let a and b be positive real numbers. Suppose P Q = a i ^ + b j ^ and P S = a i ^ - b j ^ are adjacent sides of a parallelogram P Q R S . Le2020 (Paper 2)Product of 2 vectors
  14. 14Let a = 2 i ^ + j ^ - k ^ and b = i ^ + 2 j ^ + k ^ be two vectors. Consider a vector c = a + b , , R . If the projection of c on the vector2019 (Paper 2)Product of 2 vectors
  15. 15Let a → and b → be two unit vectors such that a → . b → = 0 . For some x , y ∈ R, let c → = x a → + y b → + a → × b → . If c → = 2 and the v2018 (Paper 1)Product of 2 vectors
  16. 16Consider the cube in the first octant with sides O P , O Q and OR of length 1 , along the x-axis, y-axis and z-axis, respectively, where O (2018 (Paper 2)Product of 2 vectors
  17. 17Let O be the origin and let P Q R be an arbitrary triangle. The point S is such that O P . O Q + O R . O S = O R . O P + O Q . O S = O Q . O2017 (Paper 2)Product of 2 vectors
  18. 18Paragraph: Let be the origin, and be three unit vectors in the directions of the sides , , respectively, of a triangle . Question:2017 (Paper 2)Product of 2 vectors
  19. 19Let u ^ = u 1 i ^ + u 2 j ^ + u 3 k ^ be a unit vector in R 3 and w ^ = 1 6 i ^ + j ^ + 2 k ^ . Given that there exists a vector v in R 3 su2016 (Paper 2)Product of 2 vectors
  20. 20Let P Q R be a triangle. Let a = Q R , b = R P a n d c = P Q . If a = 12 , b = 4 3 and b c = 24 , then which of the following is (are) true 2015 (Paper 1)Product of 2 vectors
  21. 21Suppose that p , q a n d r are three non - coplanar vectors in R 3 . Let the components of a vector s along \(p, q\) and \(r\) be 4,3 and 5 2015 (Paper 2)Algebra of Vectors
  22. 22Let x , y and z be three vectors each of magnitude 2 and the angle between each pair of them is 3 . If a is a non - zero vector perpendicula2014 (Paper 1)Vector Triple Product
  23. 23Let a , b and c be three non - coplanar unit vectors such that the angle between every pair of them is 3 . If a b + b c = p a + q b + r c , 2014 (Paper 1)Scalar Triple Product
  24. 24Let PR = 3 i ^ + j ^ - 2 k ^ and SQ = i ^ - 3 j ^ - 4 k ^ determine diagonals of a parallelogram PQRS and PT = i ^ + 2 j ^ + 3 k ^ be anothe2013 (Paper 1)Scalar Triple Product
  25. 25Consider the set of eight vectors V = a i ^ + b j ^ + c k ^ : a, b, c - 1 , 1 . Three non-coplanar vectors can be chosen from V in 2 p ways.2013 (Paper 1)Algebra of Vectors
  26. 26Match List-I with List - II and select the correct answer using the code given below the lists List-I List-II A. Volume of parallelepiped de2013 (Paper 2)Vector Triple Product
  27. 27If and are unit vectors satisfying , then is2012 (Paper 1)Algebra of Vectors
  28. 28If and are vectors such that and , then a possible value of is2012 (Paper 2)Algebra of Vectors
  29. 29Let and be three vectors. A vector in the plane of and whose projection of is , is given by2011 (Paper 1)Algebra of Vectors
  30. 30The vector(s) which is/are coplanar with vectors and , are perpendicular to the vector is/are2011 (Paper 1)Vector Triple Product
  31. 31Let and be three given vectors. If is a vector such that and , then the value of is2011 (Paper 2)Algebra of Vectors
  32. 32Let and be the points on the plane with position vectors an respectively. The quadrilateral must be a2010 (Paper 1)Algebra of Vectors
  33. 33If and are vectors in space given by and , then the value of is2010 (Paper 1)Algebra of Vectors
  34. 34Two adjacent sides of a parallelogram are given by and . The side is rotated by an acute angle in the plane of the parallelogram so that bec2010 (Paper 2)Product of 2 vectors
  35. 35Preview not available - open to view this question.2010 (Paper 2)Algebra of Vectors
  36. 36If and are the unit vectors such that and , then2009 (Paper 1)Scalar Triple Product
  37. 37Match the statements/expressions given in Column I with the values given in Column II.2009 (Paper 2)Scalar Triple Product
  38. 38The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors such that . Then, the volume of the parallelo2008 (Paper 1)Scalar Triple Product
  39. 39Let two non-collinear unit vectors and form an acute angle. A point moves so that at any time the position vector (where, is the origin) is 2008 (Paper 2)Algebra of Vectors
  40. 40Paragraph: Consider the lines: Question: The unit vector perpendicular to both and is2008 (Paper 2)Product of 2 vectors
  41. 41The number of distinct real values of , for which the vectors , and are coplanar, is2007 (Paper 1)Scalar Triple Product
  42. 42Let the vectors and UP represent the sides of a regular hexagon. Statement I PQ Statement II and2007 (Paper 1)Algebra of Vectors
  43. 43Let be unit vectors such that . Which one of the following is correct?2007 (Paper 2)Algebra of Vectors
  44. 44Let . A vector coplanar to and has a projection along c of magnitude , then the vector is2006Algebra of Vectors
  45. 45Let be vector parallel to line of intersection of planes and through origin. is parallel to the vectors and and is parallel to and , then th2006Product of 2 vectors
  46. 46Match the following2006Vector Triple Product

Frequently Asked Questions

1.How many questions are available for Vector Algebra?

This chapter includes 46 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

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

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

Vector Algebra has appeared in 21 of the 21 years of JEE Advanced papers covered here, with 46 questions across 35 papers - about one per paper it appears in.

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

Of the 46 questions analysed for this chapter, 26% are easy, 54% moderate and 20% tough. 2010 had the most, with 4 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 - 18 questions (39%)
  • Algebra of Vectors - 15 questions (33%)
  • Scalar Triple Product - 9 questions (20%)
  • Scalar Triple Product has produced the most tough questions (3).
6.Is Vector Algebra's weightage in JEE Advanced going up or down?

Across all 35 papers analysed, Vector Algebra has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.