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Mathematics - Vector Algebra

Practise 72 KCET previous year questions on Vector Algebra, compiled from papers spanning 2007 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 KCET tests.

Vector Algebra has been asked in 20 of the 20 years of KCET papers analysed (2007–2026), with 72 questions in all. 49% of them were easy, 39% moderate and 13% tough. Most of its questions came from 2016, with 5 questions that year. In the last three years (2024–2026) it had 10 questions across 3 papers, about 3.3 per paper.

The chapter's 4 topics are not weighted equally: Product of 2 vectors (39 questions, 54%), Algebra of Vectors (20 questions, 28%), and Scalar Triple Product (8 questions, 11%) have been asked the most. Product of 2 vectors has also led over the last five years, with 12 questions. Product of 2 vectors has produced the most tough questions (4).

  1. 1If and , then is equal to2026Algebra of Vectors
  2. 2If and , then is2026Product of 2 vectors
  3. 3The value of for which the vectors and are orthogonal is2026Product of 2 vectors
  4. 4If and are such that is perpendicular to , then the value of is2025Product of 2 vectors
  5. 5If and , then the value of is2025Product of 2 vectors
  6. 6Consider the following statements : Statement (I) : If either or , then Statement (II) : If , then is perpendicular to . Which of the follow2025Product of 2 vectors
  7. 7The vectors and are the sides of a , The length of the median through is2024Algebra of Vectors
  8. 8The volume of the parallelopiped whose co terminous edges are and is2024Scalar Triple Product
  9. 9Let and be two unit vectors and is the angle between them. Then, is a unit vector, if2024Product of 2 vectors
  10. 10If and are three non-coplanar vectors and and are vectors defined by , then is2024Vector Triple Product
  11. 11and , then is equal to2023Product of 2 vectors
  12. 12If and , then the value of is equal to2023Product of 2 vectors
  13. 13If , then2023Product of 2 vectors
  14. 14The component of in the direction of the vector is2023Product of 2 vectors
  15. 15If and and the angle between and is , then the length of the vector is2022Product of 2 vectors
  16. 16If and , then is equal to2022Product of 2 vectors
  17. 17If , then express in the form where is parallel to and is perpendicular to , then is given by2022Algebra of Vectors
  18. 18A vector a makes equal acute angles on the coordinate axis. Then the projection of vector on is2021Algebra of Vectors
  19. 19The diagonals of a parallelogram are the vectors . and . Then the length of the shorter side of parallelogram is2021Product of 2 vectors
  20. 20If and makes an angle with a, then2021Product of 2 vectors
  21. 21If the area of the parallelogram with and as two adjacent sides is 15 sq units, then the area of the parallelogram having and as two adjacen2021Product of 2 vectors
  22. 22The order of the differential equation obtained by eliminating arbitrary constants in the family of curves is2020Algebra of Vectors
  23. 23The general solution of the differential equation is2020Product of 2 vectors
  24. 24The two vector and represent the two sides and respectively of a . The length of the median through is2020Product of 2 vectors
  25. 25The curve passing through the point given that the slope of the tangent at any point is represents2020Algebra of Vectors
  26. 26If \( | {a}|=16,| {b}|=4 \) then, \( {| {a} {b}|^{2}+| {a} {b}|^{2}} \)2019Product of 2 vectors
  27. 27If the angle between \( {a} \) and \( {b} \) is \( {2 }{3} \) and the projection of \( {a} \) in the direction of \( {b} \) is \( -2 \), the2019Product of 2 vectors
  28. 28\( [ {a}+2 {b}- {c}, {a}- {b}, {a}- {b}- {c}]= \)2019Vector Triple Product
  29. 29If \( | {a} {b}|^{2}+| {a} {b}|^{2}=144 \) and \( | {a}|=4 \), then the value of \( | {b}| \) is2018Product of 2 vectors
  30. 30If \( | {a}| \) and \( | {b}| \) are mutually perpendicular unit vectors, then \( (3| {a}|+2| {b}|) (5| {a}|-6| {b}|)= \)2018Product of 2 vectors
  31. 31If the vector \( a {i}+ {j}+ {k}, {i}+b {j}+ {k} \) and \( {i}+ {j}+c {k} \) are colpanar \( (a b c 1) \), then the value of \( a b c-(a+b+c2018Algebra of Vectors
  32. 32If \( {a}= {i}+ {j}+2 {k} ; {b}= {i}+ {j}- {k} \) are orthogonal and \( | {a}|=| {b}| \) then \( ( , )= \)2018Algebra of Vectors
  33. 33Equation of line passing through the point \( (1,2) \) and perpendicular to the line \( y=3 x-1 \)2017Algebra of Vectors
  34. 34The point on the curve \( y^{2}=x \) where the tangent makes an angle of \( / 4 \) with \( x \)-axis is2017Product of 2 vectors
  35. 35If \( y= | {array}{ccc}f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c {array} | \), then \( {d y}{d x} \) is equal to2017Product of 2 vectors
  36. 36If \( 2 {a} {b}=| {a}| | {b}| \) then the angle between \( {a} \& {b} \) is2016Product of 2 vectors
  37. 37If \( {a} \) and \( {b} \) are unit vectors then what is the angle between \( {a} \) and \( {b} \) for \( {3} {a}- {b} \) to be unit vector?2016Algebra of Vectors
  38. 38Suppose \( {a}+ {b}+ {c}=0,| {a}|=3,| {b}|=5,| {c}|=7 \), then the angle between \( {a} \& {b} \) is2016Algebra of Vectors
  39. 39If \( | {a}|=3,| {b}|=4,| {c}|=5 \) each one of \( {a}, {b} \& {c} \) is perpendicular to the sum of the remaining then \( | {a}+ {b}+ {c}| 2016Algebra of Vectors
  40. 40The value of if \( x( {i}+ {j}+ {k}) \) is a unit vector is2016Algebra of Vectors
  41. 41Slope of Normal to the curve \( y=x^{2}- {1}{x^{2}} \) at \( (-1,0) \) is2015Product of 2 vectors
  42. 42\( {1}{x^{2} (x^{4}+1 )^{3 / 4}} {dx} \) is equal to2015Algebra of Vectors
  43. 43If \( x=c t \) and \( y= {c}{t} \), find \( {d y}{d t} \) at \( t=2 \)2015Product of 2 vectors
  44. 44A straight line passes through the points \( (5,0) \) and \( (0,3) \). The length of perpendicular from the point \( (4,4) \) on the line is2014Product of 2 vectors
  45. 45Equation of circle with center \( (-a,-b) \) and radius \( {a^{2}-b^{2}} \) is2014Algebra of Vectors
  46. 46The area of the triangle formed by the lines joining the vertex of the parabola \( x^{2}=12 y \) to the ends of Latus rectum is2014Scalar Triple Product
  47. 47If and , then2013Vector Triple Product
  48. 48If and , then is equal to2013Product of 2 vectors
  49. 49If and are unit vectors such that , then is equal to2013Product of 2 vectors
  50. 50If is a vector perpendicular to both and , then2013Product of 2 vectors

Frequently Asked Questions

1.How many questions are available for Vector Algebra?

This chapter includes 72 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Vector Algebra has appeared in 20 of the 20 years of KCET papers covered here, with 72 questions across 20 papers - about 4 per paper it appears in.

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

Of the 72 questions analysed for this chapter, 49% are easy, 39% moderate and 13% tough. 2016 had the most, with 5 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 - 39 questions (54%)
  • Algebra of Vectors - 20 questions (28%)
  • Scalar Triple Product - 8 questions (11%)
  • Product of 2 vectors has produced the most tough questions (4).
6.Is Vector Algebra's weightage in KCET going up or down?

Across all 20 papers analysed, Vector Algebra has averaged about 3.6 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.