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Mathematics - Vector Algebra

Practise 190 NDA previous year questions on Vector Algebra, compiled from papers spanning 2010 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 NDA tests.

Vector Algebra has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 190 questions in all. 22% of them were easy, 77% moderate and 1% tough. Most of its questions came from 2015, with 15 questions that year. In the last three years (2024–2026) it had 26 questions across 5 papers, about 5.2 per paper.

The chapter's 4 topics are not weighted equally: Product of 2 vectors (92 questions, 48%), Algebra of Vectors (84 questions, 44%), and Scalar Triple Product (9 questions, 5%) have been asked the most. Product of 2 vectors has also led over the last five years, with 23 questions. Product of 2 vectors has produced the most tough questions (1).

  1. 1Passage: Let , , , , , be unit vectors. Question: What is the angle between and ?2026 (Phase 1)Product of 2 vectors
  2. 2Passage: Let , , , , , be unit vectors. Question: What is the angle between and ?2026 (Phase 1)Algebra of Vectors
  3. 3Passage: Let and . Question: Consider the following statements : I. , , are orthogonal in pairs. II. , , are unit vectors. Which of the stat2026 (Phase 1)Product of 2 vectors
  4. 4Passage: Let and . Question: Consider the following statements : I. II. Which of the statements given above is/are correct ?2026 (Phase 1)Product of 2 vectors
  5. 5Passage: Let , , be unit vectors. Further, is perpendicular to ; makes an angle with both and ; and . Question: What is the value of ?2026 (Phase 1)Algebra of Vectors
  6. 6Passage: Let , , be unit vectors. Further, is perpendicular to ; makes an angle with both and ; and . Question: What is the value of ?2026 (Phase 1)Algebra of Vectors
  7. 7is a triangle right-angled at . If , and are the vertices of the triangle, then what is the value of ?2025 (Phase 1)Product of 2 vectors
  8. 8Consider the following statements in respect of a vector : I. is coplanar with and . II. is perpendicular to . Which of the statements given2025 (Phase 1)Vector Triple Product
  9. 9The position vectors of three points , and are , and respectively such that . What is equal to?2025 (Phase 1)Algebra of Vectors
  10. 10The position vectors of three points , and are , and respectively, where . What is equal to?2025 (Phase 1)Product of 2 vectors
  11. 11Let , , be unit vectors. What is equal to?2025 (Phase 1)Product of 2 vectors
  12. 12For the following two (02) items: Let , and are three consecutive vertices of a parallelogram . If angle is , then what is equal to?2025 (Phase 2)Product of 2 vectors
  13. 13Let , . If and , then what is the value of ?2025 (Phase 2)Algebra of Vectors
  14. 14How many of the following can be a vector perpendicular to both the vectors and ? I. II. III. Select the correct answer.2025 (Phase 2)Product of 2 vectors
  15. 15What is the area of the parallelogram whose sides are represented by the vectors and ?2025 (Phase 2)Product of 2 vectors
  16. 16The position vectors of the vertices , , and of a quadrilateral are given by , , and respectively. What is the angle between the diagonals a2025 (Phase 2)Algebra of Vectors
  17. 17A force is applied at the point . If its moment about the point is , then what is the value of ?2025 (Phase 2)Product of 2 vectors
  18. 18Let and . If , then what is the value of ?2024 (Phase 1)Vector Triple Product
  19. 19Consider the following in respect of moment of a force: 1. The moment of force about a point is independent of point of application of force2024 (Phase 1)Algebra of Vectors
  20. 20For any vector , what is equal to?2024 (Phase 1)Vector Triple Product
  21. 21Let and are two vectors of magnitude 4 inclined at an angle , then what is the angle between and ?2024 (Phase 1)Product of 2 vectors
  22. 22What is equal to if is a null vector?2024 (Phase 2)Algebra of Vectors
  23. 23For what value of the angle between the vectors and is the quantity maximum?2024 (Phase 2)Product of 2 vectors
  24. 24Let be the angle between two unit vectors and . If is perpendicular to , then what is equal to?2024 (Phase 2)Product of 2 vectors
  25. 25Let ABCDEF be a regular hexagon. If and , then what is equal to?2024 (Phase 2)Algebra of Vectors
  26. 26The vectors and are of the same length. If taken pairwise, they form equal angles. If and , then what can be equal to? A. B. Select the corr2024 (Phase 2)Algebra of Vectors
  27. 27Paragraph: Let and . Let be such that and Question: What is equal to?2023 (Phase 1)Product of 2 vectors
  28. 28Paragraph: Let and . Let be such that and Question: What is the angle between and ?2023 (Phase 1)Product of 2 vectors
  29. 29Paragraph: The position vectors of two points A and B are and respectively. Question: What is the magnitude of ?2023 (Phase 1)Algebra of Vectors
  30. 30What is the length of projection of the vector on the vector ?2023 (Phase 2)Product of 2 vectors
  31. 31If and , then what is the value of ?2023 (Phase 2)Product of 2 vectors
  32. 32If is the angle between vectors and such that , then which one of the following is correct?2023 (Phase 2)Product of 2 vectors
  33. 33The vectors are collinear if:2023 (Phase 2)Algebra of Vectors
  34. 34Consider the following in respect of the vectors and : 1. The number of unit vectors perpendicular to both and is only one. 2. The angle bet2023 (Phase 2)Product of 2 vectors
  35. 35If and are collinear vectors, then what are the possible values of and respectively?2022 (Phase 1)Algebra of Vectors
  36. 36If are the position vectors of the vertices respectively of a triangle and is the centroid of the triangle, then what is equal to?2022 (Phase 1)Algebra of Vectors
  37. 37Consider the following statements : 1. Dot product over vector addition is distributive 2. Cross product over vector addition is distributiv2022 (Phase 1)Scalar Triple Product
  38. 38Let be three non-zero vectors such that . Consider the following statements : 1. is unique if and are given 2. is unique if and are given Wh2022 (Phase 1)Product of 2 vectors
  39. 39Let and be two unit vectors such that . If is the angle between and , then which one of the following is correct?2022 (Phase 1)Algebra of Vectors
  40. 40is a parallelogram. If and , then what is equal to?2022 (Phase 2)Algebra of Vectors
  41. 41Let and are two unit vectors such that and are perpendicular. What is the angle between and ?2022 (Phase 2)Product of 2 vectors
  42. 42Let and be unit vectors lying on the same plane. What is equal to?2022 (Phase 2)Scalar Triple Product
  43. 43What are the values of for which the angle between the vectors and is obtuse?2022 (Phase 2)Product of 2 vectors
  44. 44The position vectors of vertices and of triangle are respectively and . What is angle equal to?2022 (Phase 2)Product of 2 vectors
  45. 45A vector is equally inclined to both and axes. If the magnitude of the vector is 2 units, then what are the values of and respectively?2021 (Phase 1)Algebra of Vectors
  46. 46Consider the following statements in respect of a vector , where : 1. is perpendicular to . 2. is perpendicular to . Which of the above stat2021 (Phase 1)Algebra of Vectors
  47. 47If and are two vectors such that , then which one of the following is correct?2021 (Phase 1)Product of 2 vectors
  48. 48If and are coplanar, then what is . equal to?2021 (Phase 1)Scalar Triple Product
  49. 49Consider the following statements : 1. The cross product of two unit vectors is always a unit vector. 2. The dot product of two unit vectors2021 (Phase 1)Algebra of Vectors
  50. 50The coordinates of three consecutive vertices of a parallelogram are and . What is the area of the parallelogram?2021 (Phase 2)Product of 2 vectors

Frequently Asked Questions

1.How many questions are available for Vector Algebra?

This chapter includes 190 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Vector Algebra has appeared in 17 of the 17 years of NDA papers covered here, with 190 questions across 32 papers - about 6 per paper it appears in.

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

Of the 190 questions analysed for this chapter, 22% are easy, 77% moderate and 1% tough. 2015 had the most, with 15 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 - 92 questions (48%)
  • Algebra of Vectors - 84 questions (44%)
  • Scalar Triple Product - 9 questions (5%)
  • Product of 2 vectors has produced the most tough questions (1).
6.Is Vector Algebra's weightage in NDA going up or down?

Across all 32 papers analysed, Vector Algebra has averaged about 5.9 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 5.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.