My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
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.

53Papers
38Years
89Questions
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 46 51.7%
Easy 24 27%
Hard 16 18%
Not classified 3 3.4%

Question type distribution

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

Multiple Choices 61 68.5%
Subjective 16 18%
Numerical Answer Type (NAT) 12 13.5%

Subject weightage

Top subjects by unique question coverage.

Mathematics
89 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
89 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Vector Algebra
89 Qs

Paper coverage

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

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 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 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 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
1 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
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
2 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 1995 SCREENING
4 Qs
IIT JEE 1994
2 Qs
IIT JEE 1993
3 Qs
IIT JEE 1989
3 Qs
IIT JEE 1988
2 Qs
IIT JEE 1987
3 Qs
IIT JEE 1986
1 Qs
IIT JEE 1985
1 Qs
IIT JEE 1984
2 Qs
IIT JEE 1983
1 Qs
IIT JEE 1982
2 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 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 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 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View 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 OFFLINE20111View 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 200620061View 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 200120012View 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 1995 SCREENING19954View paper
IIT JEE 199419942View paper
IIT JEE 199319933View paper
IIT JEE 198919893View paper
IIT JEE 198819882View paper
IIT JEE 198719873View paper
IIT JEE 198619861View paper
IIT JEE 198519851View paper
IIT JEE 198419842View paper
IIT JEE 198319831View paper
IIT JEE 198219822View 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 \(\overrightarrow A = \pm 2\left( {\overrightarrow B \times \overrightarrow C } \right).\)
A
TRUE
B
FALSE
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 ..........
Write your response
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 :
A
\(0\)
B
\(\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right] + \left[ {\overrightarrow B \,\overrightarrow C \,\overrightarrow A } \right]\)
C
\(\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right]\)
D
None of these
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
$$\sum\limits_{i = 1}^{n - 1} {\left( {\overrightarrow {O{A_i}} \times {{\overrightarrow {OA} }_{i + 1}}} \right) = \left( {1 - n} \right)\left( {{{\overrightarrow {OA} }_2} \times {{\overrightarrow {OA} }_1}} \right)}$$
Write your response
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
A
\(\overrightarrow a \,.\,\overrightarrow b = 0,\overrightarrow b \,.\,\overrightarrow c = 0\)
B
\(\overrightarrow b \,.\,\overrightarrow c = 0,\overrightarrow c \,.\,\overrightarrow a = 0\)
C
\(\overrightarrow c \,.\,\overrightarrow a = 0,\overrightarrow a \,.\,\overrightarrow b = 0\)
D
\(\overrightarrow a \,.\,\overrightarrow b = \overrightarrow b \,.\,\overrightarrow c = \overrightarrow c \,.\,\overrightarrow a = 0\)
Open complete paper
6
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 \(\left[ {A\,B\,C} \right] = 0\)
A
TRUE
B
FALSE
Open complete paper
7
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 \(k.\)
A
TRUE
B
FALSE
Open complete paper
8
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 \(ABC.\)

Write your response
Open complete paper
9
1985 · Mathematics · Algebra · Vector Algebra
IIT JEE 1985
If \(\overrightarrow A \overrightarrow {\,B} \overrightarrow {\,C}\) are three non-coplannar vectors, then -
\({{\overrightarrow A .\overrightarrow B \times \overrightarrow C } \over {\overrightarrow C \times \overrightarrow A .\overrightarrow B }} + {{\overrightarrow B .\overrightarrow A \times \overrightarrow C } \over {\overrightarrow C .\overrightarrow A \times \overrightarrow B }} =\) ................
Write your response
Open complete paper
10
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
A
\(0\)
B
\(1\)
C
\({1 \over 4}\left( {a_1^2 + a_2^2 + a_2^3} \right)\left( {b_1^2 + b_2^2 + b_3^2} \right)\)
D
\({3 \over 4}\left( {a_1^2 + a_2^2 + a_3^2} \right)\left( {b_1^2 + b_2^2 + b_3^2} \right)\left( {c_1^2 + c_2^2 + c_3^2} \right)\)
Open complete paper
11
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 \(ABC\))
Write your response
Open complete paper
12
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 \({1 \over {\left( {1 - a} \right)}} + {1 \over {\left( {1 - b} \right)}} + {1 \over {\left( {1 - c} \right)}} = ..........\)
Write your response
Open complete paper
13
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
A
one
B
two
C
three
D
infinite
Open complete paper
14
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.
Write your response
Open complete paper
15
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
A
\(0\)
B
\(1\)
C
\(2\)
D
\(3\)
Open complete paper
16
1989 · Mathematics · Algebra · Vector Algebra
IIT JEE 1989
For any three vectors \({\overrightarrow a ,\,\overrightarrow b ,}\) and \({\overrightarrow c ,}\)
$$\left( {\overrightarrow a - \overrightarrow b } \right)\,.\,\left( {\overrightarrow b - \overrightarrow c } \right)\, \times \,\left( {\overrightarrow c - \overrightarrow a } \right)\, = \,2\overrightarrow {a\,} .\,\overrightarrow {b\,} \times \,\overrightarrow c .$$
A
TRUE
B
FALSE
Open complete paper
17
1989 · Mathematics · Algebra · Vector Algebra
IIT JEE 1989
In a triangle \(OAB,E\) is the midpoint of \(BO\) and \(D\) is a point on \(AB\) such that \(AD:DB=2:1.\) If \(OD\) and \(AE\) intersect at \(P,\) determine the ratio \(OP:PD\) using vector methods.
Write your response
Open complete paper
18
1989 · Mathematics · Algebra · Vector Algebra
IIT JEE 1989
If vectors \(\overrightarrow A ,\overrightarrow B ,\overrightarrow C\) are coplanar, show that \(\left| {\matrix{ {} & {\overrightarrow {a.} } & {} & {\overrightarrow {b.} } & {} & {\overrightarrow {c.} } \cr {\overrightarrow {a.} } & {\overrightarrow {a.} } & {\overrightarrow {a.} } & {\overrightarrow {b.} } & {\overrightarrow {a.} } & {\overrightarrow {c.} } \cr {\overrightarrow {b.} } & {\overrightarrow {a.} } & {\overrightarrow {b.} } & {\overrightarrow {b.} } & {\overrightarrow {b.} } & {\overrightarrow {c.} } \cr } } \right| = \overrightarrow 0\)
Write your response
Open complete paper
19
1993 · Mathematics · Algebra · Vector Algebra
IIT JEE 1993
In a triangle \(ABC, D\) and \(E\) are points on \(BC\) and \(AC\) respectively, such that \(BD=2DC\) and \(AE=3EC.\) Let \(P\) be the point of intersection of \(AD\) and \(BE.\) Find \(BP/PE\) using vector methods.
Write your response
Open complete paper
20
1993 · Mathematics · Algebra · Vector Algebra
IIT JEE 1993
Let \(\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k\) and \(\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k\) be three vectors. A vector in the plane of \({\overrightarrow b }\) and \({\overrightarrow c }\), whose projection on \({\overrightarrow a }\) is of magnitude \(\sqrt {2/3,}\) is :
A
\(2\widehat i + 3\widehat j - 3\widehat k\)
B
\(2\widehat i + 3\widehat j + 3\widehat k\)
C
\(-2\widehat i - \widehat j + 5\widehat k\)
D
\(2\widehat i + \widehat j + 5\widehat k\)
Open complete paper

Showing 20 of 89 questions