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Previous year question hub

Vector Algebra - Algebra - Mathematics Previous Year Questions

Practice Vector Algebra - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

66Papers
46Years
112Questions
1Topics

Vector Algebra question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Vector Algebra. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 61 53.5%
Easy 26 22.8%
Hard 22 19.3%
Not classified 5 4.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 61 53.5%
Subjective 22 19.3%
Numerical Answer Type (NAT) 13 11.4%
MSQ 11 9.6%
Fill in the blanks 7 6.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
112 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
112 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Vector Algebra
112 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2025 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
2 Qs
IIT JEE 2011 PAPER 2 OFFLINE
2 Qs
IIT JEE 2010 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
3 Qs
IIT JEE 2008 PAPER 1 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
2 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 MAINS
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
2 Qs
IIT JEE 2004
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
3 Qs
IIT JEE 2001 SCREENING
2 Qs
IIT JEE 2000 SCREENING
3 Qs
IIT JEE 1999
4 Qs
IIT JEE 1998
5 Qs
IIT JEE 1997
2 Qs
IIT JEE 1996
2 Qs
IIT JEE 1995 SCREENING
4 Qs
IIT JEE 1994
2 Qs
IIT JEE 1993
3 Qs
IIT JEE 1992
1 Qs
IIT JEE 1991
2 Qs
IIT JEE 1990
1 Qs
IIT JEE 1989
3 Qs
IIT JEE 1988
3 Qs
IIT JEE 1987
4 Qs
IIT JEE 1986
2 Qs
IIT JEE 1985
2 Qs
IIT JEE 1984
2 Qs
IIT JEE 1983
1 Qs
IIT JEE 1982
3 Qs
IIT JEE 1981
3 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2025 PAPER 1 ONLINE20252View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20211View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20211View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20201View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20152View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20142View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2012 PAPER 2 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20112View paper
IIT JEE 2011 PAPER 2 OFFLINE20112View paper
IIT JEE 2010 PAPER 1 OFFLINE20102View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 1 OFFLINE20091View paper
IIT JEE 2008 PAPER 1 OFFLINE20081View paper
IIT JEE 2008 PAPER 2 OFFLINE20083View paper
IIT JEE 2007 PAPER 1 OFFLINE20072View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420041View paper
IIT JEE 2004 SCREENING20042View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 200220021View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 200120013View paper
IIT JEE 2001 SCREENING20012View paper
IIT JEE 2000 SCREENING20003View paper
IIT JEE 199919994View paper
IIT JEE 199819985View paper
IIT JEE 199719972View paper
IIT JEE 199619962View paper
IIT JEE 1995 SCREENING19954View paper
IIT JEE 199419942View paper
IIT JEE 199319933View paper
IIT JEE 199219921View paper
IIT JEE 199119912View paper
IIT JEE 199019901View paper
IIT JEE 198919893View paper
IIT JEE 198819883View paper
IIT JEE 198719874View paper
IIT JEE 198619862View paper
IIT JEE 198519852View paper
IIT JEE 198419842View paper
IIT JEE 198319831View paper
IIT JEE 198219823View paper
IIT JEE 198119813View paper

All Vector Algebra previous year questions

Practice every matching question in batches of 20, with every available option.

1
1981 · Mathematics · Algebra · Vector Algebra
IIT JEE 1981
Let \(\overrightarrow A ,\overrightarrow B\) and \({\overrightarrow C }\) be unit vectors suppose that \(\overrightarrow A .\overrightarrow B = \overrightarrow A .\overrightarrow C = 0,\) and thatthe angle between \({\overrightarrow B }\) and \({\overrightarrow C }\) is \(\pi /6.\) Then \(\overrightarrow A = \pm 2\left( {\overrightarrow B \times \overrightarrow C } \right).\)
Open complete paper
2
1981 · Mathematics · Algebra · Vector Algebra
IIT JEE 1981
Let \(\overrightarrow A ,\overrightarrow B ,\overrightarrow C\) be vectors of length \(3, 4, 5\) respectively. Let \(\overrightarrow A\) be perpendicular to \(\overrightarrow B + \overrightarrow C ,\overrightarrow B\) to \(\overrightarrow C + \overrightarrow A\) to \(\overrightarrow A + \overrightarrow B .\) Then the length of vector \(\overrightarrow A + \overrightarrow B + \overrightarrow C\) is ..........
Open complete paper
3
1981 · Mathematics · Algebra · Vector Algebra
IIT JEE 1981
The scalar \(\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow A + \overrightarrow B + \overrightarrow C } \right)\) equals :
Open complete paper
4
1982 · Mathematics · Algebra · Vector Algebra
IIT JEE 1982
\({A_1},{A_2},.................{A_n}\) are the vertices of a regular plane polygon with \(n\) sides and \(O\) is its centre. Show that
$$\sum\limits_{i = 1}^{n - 1} {\left( {\overrightarrow {O{A_i}} \times {{\overrightarrow {OA} }_{i + 1}}} \right) = \left( {1 - n} \right)\left( {{{\overrightarrow {OA} }_2} \times {{\overrightarrow {OA} }_1}} \right)}$$
Open complete paper
5
1982 · Mathematics · Algebra · Vector Algebra
IIT JEE 1982
For non-zero vectors \({\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },\) \(\left| {\left( {\overrightarrow a \times \overrightarrow b } \right).\overrightarrow c } \right| = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\) holds if and only if
Open complete paper
6
1982 · Mathematics · Algebra · Vector Algebra
IIT JEE 1982
Find all values of \(\lambda\) such that \(x, y, z,\)\(\, \ne\)\((0,0,0)\) and
$$\left( {\overrightarrow i + \overrightarrow j + 3\overrightarrow k } \right)x + \left( {3\overrightarrow i - 3\overrightarrow j + \overrightarrow k } \right)y + \left( { - 4\overrightarrow i + 5\overrightarrow j } \right)z$$
\(= \lambda \left( {x\overrightarrow i \times \overrightarrow j \,\,y + \overrightarrow k \,z} \right)\) where \(\overrightarrow i ,\,\,\overrightarrow j ,\,\,\overrightarrow k\) are unit vectors along the coordinate axes.
Open complete paper
7
1983 · Mathematics · Algebra · Vector Algebra
IIT JEE 1983
If \(X.A=0, X.B=0, X.C=0\) for some non-zero vector \(X,\) then \(\left[ {A\,B\,C} \right] = 0\)
Open complete paper
8
1984 · Mathematics · Algebra · Vector Algebra
IIT JEE 1984
The points with position vectors \(a+b,\) \(a-b,\) and \(a+kb\) are collinear for all real values of \(k.\)
Open complete paper
9
1984 · Mathematics · Algebra · Vector Algebra
IIT JEE 1984
\(A, B, C\) and \(D,\) are four points in a plane with position vectors \(a, b, c\) and \(d\) respectively such that \(\left( {\overrightarrow a - \overrightarrow d } \right)\left( {\overrightarrow b - \overrightarrow c } \right) = \left( {\overrightarrow b - \overrightarrow d } \right)\left( {\overrightarrow c - \overrightarrow a } \right) = 0\)

The point \(D,\) then, is the ................ of the triangle \(ABC.\)

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10
1985 · Mathematics · Algebra · Vector Algebra
IIT JEE 1985
If \(\overrightarrow A \overrightarrow {\,B} \overrightarrow {\,C}\) are three non-coplannar vectors, then -
\({{\overrightarrow A .\overrightarrow B \times \overrightarrow C } \over {\overrightarrow C \times \overrightarrow A .\overrightarrow B }} + {{\overrightarrow B .\overrightarrow A \times \overrightarrow C } \over {\overrightarrow C .\overrightarrow A \times \overrightarrow B }} =\) ................
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11
1985 · Mathematics · Algebra · Vector Algebra
IIT JEE 1985
If \(\overrightarrow A = \left( {1,1,1} \right),\,\,\overrightarrow C = \left( {0,1, - 1} \right)\) are given vectors, then a vector \(B\) satifying the equations \(\overrightarrow A \times \overrightarrow B = \overrightarrow {\,C}\) and \(\overrightarrow A .\overrightarrow B = \overrightarrow {3\,}\) ..........
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12
1986 · Mathematics · Algebra · Vector Algebra
IIT JEE 1986
Let \(\overrightarrow a = {a_1}i + {a_2}j + {a_3}k,\,\,\,\overrightarrow b = {b_1}i + {b_2}j + {b_3}k\) and \(\overrightarrow c = {c_1}i + {c_2}j + {c_3}k\) be three non-zero vectors such that \(\overrightarrow c\) is a unit vector perpendicular to both the vectors \(\overrightarrow a\) and \(\overrightarrow b .\) If the angle between \(\overrightarrow a\) and \(\overrightarrow b\) is \({\pi \over 6},\) then
\({\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{b_1}} & {{b_2}} & {{b_3}} \cr {{c_1}} & {{c_2}} & {{c_3}} \cr } } \right|^2}\) is equal to
Open complete paper
13
1986 · Mathematics · Algebra · Vector Algebra
IIT JEE 1986
The position vectors of the points \(A, B, C\) and \(D\) are \(3\widehat i - 2\widehat j - \widehat k,\,2\widehat i + 3\widehat j - 4\widehat k,\, - \widehat i + \widehat j + 2\widehat k\) and \(4\widehat i + 5\widehat j + \lambda \widehat k,\)
respectively. If the points \(A, B, C\) and \(D\) lie on a plane, find the value of \(\lambda .\)
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14
1987 · Mathematics · Algebra · Vector Algebra
IIT JEE 1987
If \(A, B, C, D\) are any four points in space, prove that -
\(\left| {\overrightarrow {AB} \times \overrightarrow {CD} + \overrightarrow {BC} \times \overrightarrow {AD} + \overrightarrow {CA} \times \overrightarrow {BD} } \right| = 4\) (area of triangle \(ABC\))
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15
1987 · Mathematics · Algebra · Vector Algebra
IIT JEE 1987
If the vectors \(a\widehat i + \widehat j + \widehat k,\,\,\widehat i + b\widehat j + \widehat k\) and \(\widehat i + \widehat j + c\widehat k\)
\(\left( {a \ne b \ne c \ne 1} \right)\) are coplannar, then the value of \({1 \over {\left( {1 - a} \right)}} + {1 \over {\left( {1 - b} \right)}} + {1 \over {\left( {1 - c} \right)}} = ..........\)
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16
1987 · Mathematics · Algebra · Vector Algebra
IIT JEE 1987
The number of vectors of unit length perpendicular to vectors \(\overrightarrow a = \left( {1,1,0} \right)\) and \(\overrightarrow b = \left( {0,1,1} \right)\) is
Open complete paper
17
1987 · Mathematics · Algebra · Vector Algebra
IIT JEE 1987
Let \(b = 4\widehat i + 3\widehat j\) and \(\overrightarrow c\) be two vectors perpendicular to each other in the \(xy\)-plane. All vectors in the same plane having projecttions \(1\) and \(2\) along \(\overrightarrow b\) and \(\overrightarrow c,\) respectively, are given by ...........
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18
1988 · Mathematics · Algebra · Vector Algebra
IIT JEE 1988
Let \(OA\) \(CB\) be a parallelogram with \(O\) at the origin and \(OC\) a diagonal. Let \(D\) be the midpoint of \(OA.\) Using vector methods prove that \(BD\) and \(CO\) intersect in the same ratio. Determine this ratio.
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19
1988 · Mathematics · Algebra · Vector Algebra
IIT JEE 1988
Let \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c ,\) be three non-coplanar vectors and \(\overrightarrow p ,\overrightarrow q ,\overrightarrow r,\) are vectors defined by the relations \(\overrightarrow p = {{\overrightarrow b \times \overrightarrow c } \over {\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right]}},\,\,\overrightarrow q = {{\overrightarrow c \times \overrightarrow a } \over {\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right]}},\,\,\overrightarrow r = {{\overrightarrow a \times \overrightarrow b } \over {\left[ {\overrightarrow a \overrightarrow b \overrightarrow c } \right]}}\) then the value of the expression \(\left( {\overrightarrow a + \overrightarrow b } \right).\overrightarrow p + \left( {\overrightarrow b + \overrightarrow c } \right).\overrightarrow q + \left( {\overrightarrow c + \overrightarrow a } \right),\overrightarrow r\) is equal to
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20
1988 · Mathematics · Algebra · Vector Algebra
IIT JEE 1988
The components of a vector \(\overrightarrow a\) along and perpendicular to a non-zero vector \(\overrightarrow b\) are ......and .....respectively.
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Showing 20 of 112 questions