My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
Previous year question hub

Vector Algebra - Mechanics - Physics Previous Year Questions

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

37Papers
10Years
39Questions
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.

Easy 23 59%
Medium 16 41%

Question type distribution

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

Multiple Choices 26 66.7%
Numerical Answer Type (NAT) 13 33.3%

Subject weightage

Top subjects by unique question coverage.

Physics
39 Qs

Most asked topics

Top topics across the included previous year papers.

Mechanics
39 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Vector Algebra
39 Qs

Paper coverage

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

JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
2 Qs
JEE Main 2021 (Online) 25th February Evening Shift
1 Qs
JEE Main 2021 (Online) 25th February Morning Shift
1 Qs
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
AIEEE 2004
1 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20191View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
AIEEE 200420041View paper

All Vector Algebra previous year questions

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

1
2004 · Physics · Mechanics · Vector Algebra
AIEEE 2004
If \(\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A\), then the angle beetween A and B is
A
\({\pi \over 2}\)
B
\({\pi \over 3}\)
C
\(\pi\)
D
\({\pi \over 4}\)
Open complete paper
2
2018 · Physics · Mechanics · Vector Algebra
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
Let \(\overrightarrow A\) = \(\left( {\widehat i + \widehat j} \right)\) and, \(\overrightarrow B = \left( {2\widehat i - \widehat j} \right).\) The magnitude of a coplanar vector \(\overrightarrow C\) such that \(\overrightarrow A .\overrightarrow C = \overrightarrow B .\overrightarrow C = \overrightarrow A .\overrightarrow B ,\) is given by :
A
\(\sqrt {{{10} \over 9}}\)
B
\(\sqrt {{{5} \over 9}}\)
C
\(\sqrt {{{20} \over 9}}\)
D
\(\sqrt {{{9} \over 12}}\)
Open complete paper
3
2019 · Physics · Mechanics · Vector Algebra
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
Two vectors \(\overrightarrow A\) and \(\overrightarrow B\) have equal magnitudes. The magnitude of \(\left( {\overrightarrow A + \overrightarrow B } \right)\) is 'n' times the magnitude of \(\left( {\overrightarrow A - \overrightarrow B } \right)\) . The angle between \({\overrightarrow A }\) and \({\overrightarrow B }\) is -
A
\({\sin ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]\)
B
\({\sin ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]\)
C
\({\cos ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]\)
D
\({\cos ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]\)
Open complete paper
4
2019 · Physics · Mechanics · Vector Algebra
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -

JEE Main 2019 (Online) 10th January Morning Slot Physics - Vector Algebra Question 37 English
A
\({1 \over 2}a\left( {\widehat k - \widehat i} \right)\)
B
\({1 \over 2}a\left( {\widehat j - \widehat i} \right)\)
C
\({1 \over 2}a\left( {\widehat j - \widehat k} \right)\)
D
\({1 \over 2}a\left( {\widehat i - \widehat k} \right)\)
Open complete paper
5
2019 · Physics · Mechanics · Vector Algebra
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
Let \(\left| {\mathop {{A_1}}\limits^ \to } \right| = 3\), \(\left| {\mathop {{A_2}}\limits^ \to } \right| = 5\) and \(\left| {\mathop {{A_1}}\limits^ \to + \mathop {{A_2}}\limits^ \to } \right| = 5\). The value of \(\left( {2\mathop {{A_1}}\limits^ \to + 3\mathop {{A_2}}\limits^ \to } \right)\left( {3\mathop {{A_1}}\limits^ \to - \mathop {2{A_2}}\limits^ \to } \right)\) is :-
A
–118.5
B
–112.5
C
–99.5
D
–106.5
Open complete paper
6
2020 · Physics · Mechanics · Vector Algebra
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT
The sum of two forces \(\overrightarrow P\) and \(\overrightarrow Q\) is \(\overrightarrow R\) such that \(\left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right|\) . The angle \(\theta\) (in degrees) that the resultant of 2\({\overrightarrow P }\) and \({\overrightarrow Q }\) will make with \({\overrightarrow Q }\) is , ..............
Enter a numerical response
Open complete paper
7
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
Two vectors \({\overrightarrow P }\) and \({\overrightarrow Q }\) have equal magnitudes. If the magnitude of \({\overrightarrow P + \overrightarrow Q }\) is n times the magnitude of \({\overrightarrow P - \overrightarrow Q }\), then angle between \({\overrightarrow P }\) and \({\overrightarrow Q }\) is :
A
\({\sin ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)\)
B
\({\cos ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)\)
C
\({\sin ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)\)
D
\({\cos ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)\)
Open complete paper
8
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
If \(\overrightarrow A\) and \(\overrightarrow B\) are two vectors satisfying the relation \(\overrightarrow A\) . \(\overrightarrow B\) = \(\left| {\overrightarrow A \times \overrightarrow B } \right|\). Then the value of \(\left| {\overrightarrow A - \overrightarrow B } \right|\) will be :
A
\(\sqrt {{A^2} + {B^2} + \sqrt 2 AB}\)
B
\(\sqrt {{A^2} + {B^2}}\)
C
\(\sqrt {{A^2} + {B^2} - \sqrt 2 AB}\)
D
\(\sqrt {{A^2} + {B^2} + 2AB}\)
Open complete paper
9
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
Three particles P, Q and R are moving along the vectors \(\overrightarrow A = \widehat i + \widehat j\), \(\overrightarrow B = \widehat j + \widehat k\) and \(\overrightarrow C = - \widehat i + \widehat j\) respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector \(\overrightarrow A\) and \(\overrightarrow B\). Similarly particle Q is moving normal to the plane which contains vector \(\overrightarrow A\) and \(\overrightarrow C\). The angle between the direction of motion of P and Q is \({\cos ^{ - 1}}\left( {{1 \over {\sqrt x }}} \right)\). Then the value of x is _______________.
Enter a numerical response
Open complete paper
10
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
What will be the projection of vector \(\overrightarrow A = \widehat i + \widehat j + \widehat k\) on vector \(\overrightarrow B = \widehat i + \widehat j\) ?
A
\(\sqrt 2 (\widehat i + \widehat j + \widehat k)\)
B
\((\widehat i + \widehat j)\)
C
\(\sqrt 2 (\widehat i + \widehat j)\)
D
\(2(\widehat i + \widehat j + \widehat k)\)
Open complete paper
11
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
Two vectors \(\overrightarrow X\) and \(\overrightarrow Y\) have equal magnitude. The magnitude of (\(\overrightarrow X\) \(-\) \(\overrightarrow Y\)) is n times the magnitude of (\(\overrightarrow X\) + \(\overrightarrow Y\)). The angle between \(\overrightarrow X\) and \(\overrightarrow Y\) is :
A
\({\cos ^{ - 1}}\left( {{{ - {n^2} - 1} \over {{n^2} - 1}}} \right)\)
B
\({\cos ^{ - 1}}\left( {{{{n^2} - 1} \over { - {n^2} - 1}}} \right)\)
C
\({\cos ^{ - 1}}\left( {{{{n^2} + 1} \over { - {n^2} - 1}}} \right)\)
D
\({\cos ^{ - 1}}\left( {{{{n^2} + 1} \over {{n^2} - 1}}} \right)\)
Open complete paper
12
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
Match List - I with List - II

JEE Main 2021 (Online) 25th July Morning Shift Physics - Vector Algebra Question 27 English
Choose the correct answer from the options given below :
A
(a) \(\to\) (iv), (b) \(\to\) (i), (c) \(\to\) (iii), (d) \(\to\) (ii)
B
(a) \(\to\) (iv), (b) \(\to\) (iii), (c) \(\to\) (i), (d) \(\to\) (ii)
C
(a) \(\to\) (iii), (b) \(\to\) (ii), (c) \(\to\) (iv), (d) \(\to\) (i)
D
(a) \(\to\) (i), (b) \(\to\) (iv), (c) \(\to\) (ii), (d) \(\to\) (iii)
Open complete paper
13
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT
The angle between vector \(\left( {\overrightarrow A } \right)\) and \(\left( {\overrightarrow A - \overrightarrow B } \right)\) is :

JEE Main 2021 (Online) 26th August Evening Shift Physics - Vector Algebra Question 23 English
A
\({\tan ^{ - 1}}\left( {{{ - {B \over 2}} \over {A - B{{\sqrt 3 } \over 2}}}} \right)\)
B
\({\tan ^{ - 1}}\left( {{A \over {0.7B}}} \right)\)
C
\({\tan ^{ - 1}}\left( {{{\sqrt 3 B} \over {2A - B}}} \right)\)
D
\({\tan ^{ - 1}}\left( {{{B\cos \theta } \over {A - B\sin \theta }}} \right)\)
Open complete paper
14
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
The magnitude of vectors \(\overrightarrow {OA}\), \(\overrightarrow {OB}\) and \(\overrightarrow {OC}\) in the given figure are equal. The direction of \(\overrightarrow {OA}\) + \(\overrightarrow {OB}\) \(-\) \(\overrightarrow {OC}\) with x-axis will be :

JEE Main 2021 (Online) 26th August Morning Shift Physics - Vector Algebra Question 24 English
A
\({\tan ^{ - 1}}{{(1 - \sqrt 3 - \sqrt 2 )} \over {(1 + \sqrt 3 + \sqrt 2 )}}\)
B
\({\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 + \sqrt 3 - \sqrt 2 )}}\)
C
\({\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 - \sqrt 3 + \sqrt 2 )}}\)
D
\({\tan ^{ - 1}}{{(1 + \sqrt 3 - \sqrt 2 )} \over {(1 - \sqrt 3 - \sqrt 2 )}}\)
Open complete paper
15
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
The resultant of these forces \(\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS}\) and \(\overrightarrow {OT}\) is approximately .......... N.

[Take \(\sqrt 3 = 1.7\), \(\sqrt 2 = 1.4\) Given \(\widehat i\) and \(\widehat j\) unit vectors along x, y axis]

JEE Main 2021 (Online) 27th August Morning Shift Physics - Vector Algebra Question 22 English
A
\(9.25\widehat i + 5\widehat j\)
B
\(3\widehat i + 15\widehat j\)
C
\(2.5\widehat i - 14.5\widehat j\)
D
\(- 1.5\widehat i - 15.5\widehat j\)
Open complete paper
16
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that \(\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|\), then \(\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} = 4\overrightarrow {AO} + \overrightarrow {OB} + \overrightarrow {OC}\)

Reason R : Polygon law of vector addition yields \(\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CD} + \overrightarrow {AD} = 2\overrightarrow {AO}\)

JEE Main 2021 (Online) 27th July Morning Shift Physics - Vector Algebra Question 25 English
In the light of the above statements, choose the most appropriate answer from the options given below :
A
A is correct but R is not correct.
B
A is not correct but R is correct.
C
Both A and R are correct and R is the correct explanation of A.
D
Both A and R are correct but R is not the correct explanation of A.
Open complete paper
17
2021 · Physics · Mechanics · Vector Algebra
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
Statement I :

Two forces \(\left( {\overrightarrow P + \overrightarrow Q } \right)\) and \(\left( {\overrightarrow P - \overrightarrow Q } \right)\) where \(\overrightarrow P \bot \overrightarrow Q\), when act at an angle \(\theta\)1 to each other, the magnitude of their resultant is \(\sqrt {3({P^2} + {Q^2})}\), when they act at an angle \(\theta\)2, the magnitude of their resultant becomes \(\sqrt {2({P^2} + {Q^2})}\). This is possible only when \({\theta _1} < {\theta _2}\).

Statement II :

In the situation given above.

\(\theta\)1 = 60\(^\circ\) and \(\theta\)2 = 90\(^\circ\)

In the light of the above statements, choose the most appropriate answer from the options given below :-
A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false.
Open complete paper
18
2022 · Physics · Mechanics · Vector Algebra
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT

Which of the following relations is true for two unit vector \(\widehat A\) and \(\widehat B\) making an angle \(\theta\) to each other?

A
\(|\widehat A + \widehat B| = |\widehat A - \widehat B|\tan {\theta \over 2}\)
B
\(|\widehat A - \widehat B| = |\widehat A + \widehat B|\tan {\theta \over 2}\)
C
\(|\widehat A + \widehat B| = |\widehat A - \widehat B|cos{\theta \over 2}\)
D
\(|\widehat A - \widehat B| = |\widehat A + \widehat B|\cos {\theta \over 2}\)
Open complete paper
19
2022 · Physics · Mechanics · Vector Algebra
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT

\(\overrightarrow A\) is a vector quantity such that \(|\overrightarrow A |\) = non-zero constant. Which of the following expression is true for \(\overrightarrow A\) ?

A
\(\overrightarrow A \,.\,\overrightarrow A = 0\)
B
\(\overrightarrow A \times \overrightarrow A < 0\)
C
\(\overrightarrow A \times \overrightarrow A = 0\)
D
\(\overrightarrow A \times \overrightarrow A > 0\)
Open complete paper
20
2022 · Physics · Mechanics · Vector Algebra
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT

If \(\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m}\) and \(\vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}\). The magnitude of component of vector \(\vec{A}\) along vector \(\vec{B}\) will be ____________ \(\mathrm{m}\).

Enter a numerical response
Open complete paper

Showing 20 of 39 questions