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Mathematics - Vector Algebra

Practise 100 NTA Abhyas (JEE Main) questions on Vector Algebra. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Vector Algebra has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 100 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let V → θ = cos ⁡ θ + sec ⁡ θ a ^ + cos ⁡ θ - s e c θ b ^ , where a ^ and b ^ are unit vectors and the angle between a ^ and b ^ is 60 o , t
  2. 2Let the volume of a parallelepiped whose coterminous edges are given by u → = i ^ + j ^ + λ k ^ , v → = i ^ + j ^ + 3 k ^ and w → = 2 i ^ +
  3. 3Let A , B , C and D are 4 points in space satisfying the equation A B → ⋅ C D → = k A D → 2 + B C → 2 - A C → 2 - B D → 2 , then the value o
  4. 4Let V 1 = i ^ + a j ^ + k ^ , V 2 = j ^ + a k ^ and V 3 = a i ^ + k ^ , a 0 . If V 1 V 2 V 3 is minimum, then the value of a is
  5. 5The value of a , such that the volume of the parallelopiped formed by the vectors i ^ + j ^ + k ^ , j ^ + a k ^ and a i ^ + k ^ becomes mini
  6. 6Let a → = i ^ + 2 j ^ + 3 k ^ , b → = i ^ - j ^ + 2 k ^ and c → = x - 2 i ^ - x - 3 j ^ - k ^ . If c → lies in the plane of a → and b → , th
  7. 7Let a → = 2 i ^ - j ^ + 3 k ^ , b → = i ^ + j ^ - 4 k ^ and non-zero vector c → are such that a → × b → × c → = a → × b → × c → , then vecto
  8. 8A vector r is equally inclined with the vectors a = cos i ^ + sin j ^ , b = - sin i ^ + cos j ^ and c = k ^ , then the angle between r and a
  9. 9Let U = i ^ + j ^ , V = i ^ - j ^ and W = 3 i ^ + 5 j ^ + 3 k ^ . If n ^ is a unit vector such that U n ^ = 0 and V n ^ = 0 , then W n ^ is
  10. 10If two points P and Q are on the curve y = 2 x + 2 , such that O P → ⋅ i ^ = − 1 and O Q → ⋅ i ^ = 2 , where i ^ is a unit vector along the
  11. 11If the line x - 1 2 = y - 2 3 = z - 4 4 intersect the x y and y z plane at points A and B respectively. If the volume of the tetrahedron O A
  12. 12Let O be an interior point of triangle A B C, such that 2 O A → + 3 O B → + 4 O C → = 0, then the ratio of the area of ∆ A B C to the area o
  13. 13In a A B C , the sides B C , C A and A B are consecutive positive integers in increasing order. Let a , b and c are position vectors of the
  14. 14Two points P and Q are lying on the curve y = l o g 2 x + 3 in x y plane such that O P → ⋅ i ^ = 1 and O Q → ⋅ j ^ = 3 , then the value of O
  15. 15Let = 1 a i ^ + 4 b j ^ + b k ^ and = b i ^ + a j ^ + 1 b k ^ a , b 0 , then the maximum value of 12 6 + is
  16. 16Let 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 v
  17. 17Let a → = 2 i ^ + 3 j ^ + 4 k ^ , b → = i ^ - 2 j ^ + k ^ and c → = i ^ + j ^ - k ^ . If r → × a → = b → and r → ⋅ c → = 3 , then the value
  18. 18Let 2 a → = b → × c → + 2 b → where a → , b → and c → are three unit vectors, then sum of all possible values of 3 a → + 4 b → + 5 c → is
  19. 19Let a → , b → and c → are three non-collinear vectors in a plane such that a → = 2 , b → = 5 and c → = 29 . If the angle between a → and c →
  20. 20Let a → = i ^ + 2 j ^ + 3 k ^ , b → = 2 i ^ + 3 j ^ + k ^ , c → = k ^ + i ^ and x → × b → = a → × c → × b → . If x → ⋅ a → = 0 , then x → is
  21. 21A straight line L cuts the sides A B , A C , A D of a parallelogram A B C D at B 1 , C 1 , D 1 respectively. If A B 1 = 1 A B , A D 1 = 2 A
  22. 22If a → , b → , c → be three unit vectors perpendicular to each other, then 2 a → + 3 b → + 4 c → ⋅ a → × b → + 5 b → × c → + 6 c → × a → is
  23. 23Consider a parallelogram constructed on the vectors A → = 5 p → + 2 q → and B → = p → - 3 q → . If p → = 2 , q → = 5 , the angle between p →
  24. 24Let x → and y → are 2 non-zero and non-collinear vectors, then the largest value of k such that the non-zero vectors k 2 - 5 k + 6 x → + k -
  25. 25If r → ⋅ i ^ = 2 r → ⋅ j ^ = 4 r → ⋅ k ^ and | r → | = 84 , then the value of r → ⋅ 2 i ^ - 3 j ^ + k ^ may be
  26. 26Consider two vectors a = 3 i ^ - 2 j ^ + 4 k ^ and b = j ^ + 2 k ^ . If c is a unit vector and k be the maximum value of a b c , then the va
  27. 27Let P and Q are two points in the x y plane on the curve y = x 11 – 2 x 7 + 7 x 3 + 11 x + 6 such that O P → ⋅ i ^ = 5 , O Q → ⋅ i ^ = - 5 ,
  28. 28If x → and y → be two non-collinear vectors and a triangle A B C with side lengths a , b , c satisfy the vector equation 20 a - 15 b x → + 1
  29. 29If a and b are vectors perpendicular to each other and a = 2 , b = 3 and c a = b , then the least value of c - a is
  30. 30Let a , b and c be three vectors such that a = 2 , b = 4 , c = 1 and b c = 15 . If b = 2 c + a , then the value of is equal to (here, the an
  31. 31Let a → , b → and c → be three vectors such that a → = 2 , b → = 1 and c → = 3 . If the projection of b → along a → is double of the project
  32. 32If a → , b → and c → are three vectors, such that a → = 2 , b → = 3 , c → = 4 , a → ⋅ c → = 0 , a → ⋅ b → = 0 and the angle between b → and
  33. 33Let a and b are two vectors such that a = 2 , b = 3 and a b = 4 . If c = 3 a b - 4 b , then c is equal to
  34. 34If a line passing through - 2 , 1 , and 4,1 , 2 is perpendicular to the vector 3 i ^ - 4 j ^ + 5 k ^ and parallel to the plane containing ve
  35. 35If a 1 → , a 2 → , a 3 → and b 1 → , b 2 → , b 3 → be two sets of non-coplanar vectors, such that a p → ⋅ b q → = 0 i f p ≠ q 4 i f p = q fo
  36. 36Let A , B , C and D are any 4 points in space. If A B → × C D → + B C → × A D → + C A → × B D → = λ Δ A B C , where Δ A B C is the area of t
  37. 37Let Δ O A B be an equilateral triangle with side length unity ( O being the origin). Also, M and N are the points of trisection of A B , M b
  38. 38For three vectors a , b and c , if | a | = 2 , | b | = 1 , a b = c and b c = a , then the value of a + b b + c c + a is equal to
  39. 39A point , , satisfies the equation of the plane 3 x + 4 y + 7 z = 3 . The value of , such that p = i ^ + j ^ + k ^ satisfies the relation j
  40. 40Let a → = i ^ + j ^ + k ^ , b → = i ^ + 4 j ^ - k ^ and c → = i ^ + j ^ + 2 k ^ . If S → be a unit vector, then the magnitude of the vector
  41. 41Let a , b , c be three vectors of magnitude 3 , 4 , 5 respectively, satisfying a b c = 60 . If a + 2 b + 3 c a c b + b = , then is equal to
  42. 42The point of intersection of the lines r → = 7 i ˙ ^ + 10 j ˙ ^ + 13 k ^ + s ( 2 i ˙ ^ + 3 j ˙ ^ + 4 k ^ ) and r → = 3 i ˙ ^ + 5 j ˙ ^ + 7 k
  43. 43Let p ^ q p ^ + p ^ q q = x 2 + y 2 q + 14 - 4 x - 6 y p ^ , where p ^ and q are non-collinear vectors ( p ^ is a unit vector) and x , y are
  44. 44Let a , b , c be three non-zero, non-coplanar vectors and p , q , r be three vectors given by p = a + 2 b - 2 c , q = 3 a + b - 3 c and r =
  45. 45Let P R → = 3 i ^ + j ^ - 2 k ^ and S Q → = i ^ - 3 j ^ - 4 k ^ represent the diagonals of the parallelogram P Q R S . If P T → = 2 i ^ - j
  46. 46Given a → , b → and c → are 3 vectors such that b → , c → are parallel unit vectors and a → = 3 . If a → + λ c → = 4 b → , then the sum of a
  47. 47Let a and b are unit vectors such that a + b = 3 2 , then the value of 2 a + 7 b 4 a + 3 b + 2020 a b is equal to
  48. 48If for a plane, x , y , z intercepts are 8 , 4 , 4 respectively, then the length of the perpendicular from the origin on to the plane is
  49. 49Let p → = 2 i ^ + j ^ - 2 k ^ , q → = i ^ + j ^ . If r → is a vector such that p → . r → = r → , r → - p → = 2 2 and the angle between p → ×
  50. 50If a → , b → and c → are three vectors such that 3 a → + 4 b → + 6 c → = 0 → , a → = 3 , b → = 3 and c → = 4 , then the value of - 864 a → .

Frequently Asked Questions

1.How many questions are available for Vector Algebra?

This chapter includes 100 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Vector Algebra questions in NTA Abhyas (JEE Main)?

Of the 100 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.