Vector Algebra PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 238 recent questions

MathematicsAlgebra2017-2026

All Vector Algebra PYQs Last 5 Years Create chapter test

Practice 238 JEE Main Mathematics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

238

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

161

Last 5 Years

2022-2026

238

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

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2025

2026

202148 max PYQs/year2026

Question Types

238PYQs

MCQ76.5%

INTEGER23.5%

Difficulty Mix

#1 Medium203

#2 Hard21

#3 Easy14

161 in last 5 years238 in last 10 years

Last 10 Years Vector Algebra Questions

Showing 38 of 238 filtered questions.

1Vector Algebra

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three vectors such that \(\left| {\overrightarrow a } \right| = \sqrt 3\),
$$\left| {\overrightarrow b } \right| = 5,\overrightarrow b .\overrightarrow c = 1...

INTEGER+4 / -02020

2Vector Algebra

Let the volume of a parallelopiped whose
coterminous edges are given by
\(\overrightarrow u = \widehat i + \widehat j + \lambda \widehat k\), \(\overrightarrow v = \widehat i + \widehat j + 3\widehat k\) and
$$\overrightarrow w = 2\wideh...

3Vector Algebra

Let \(\overrightarrow a = \widehat i - 2\widehat j + \widehat k\) and \(\overrightarrow b = \widehat i - \widehat j + \widehat k\) be two
vectors. If \(\overrightarrow c\) is a vector such that $$\overrightarrow b \times \overrightarrow...

4Vector Algebra

A vector \(\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k\left( {\alpha ,\beta \in R} \right)\) lies in the plane of the vectors, \(\overrightarrow b = \widehat i + \widehat j\) and $$\overrightarrow c = \wideha...

5Vector Algebra

Let \(\overrightarrow a\)
, \(\overrightarrow b\)
and \(\overrightarrow c\)
be three unit vectors such that
\(\overrightarrow a + \vec b + \overrightarrow c = \overrightarrow 0\). If $$\lambda = \overrightarrow a .\vec b + \vec b.\...

6Vector Algebra

If \(\overrightarrow a\)
and \(\overrightarrow b\)
are unit vectors, then the greatest value of
\(\sqrt 3 \left| {\overrightarrow a + \overrightarrow b } \right| + \left| {\overrightarrow a - \overrightarrow b } \right|\) is_____.

INTEGER+4 / -02020

7Vector Algebra

If \(\overrightarrow x\) and \(\overrightarrow y\) be two non-zero vectors such that
\(\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|\) and $${2\overrightarrow x + \lambda \overrightarrow y...

INTEGER+4 / -02020

8Vector Algebra

If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\overrightarrow a = \widehat i + \widehat j + n\widehat k\), \(\overrightarrow b = 2\widehat i + 4\widehat j - n\widehat k\) and $$\overrightarrow c = ...

9Vector Algebra

Let the vectors \(\overrightarrow a\), \(\overrightarrow b\), \(\overrightarrow c\)
be such that
\(\left| {\overrightarrow a } \right| = 2\), \(\left| {\overrightarrow b } \right| = 4\)
and \(\left| {\overrightarrow c } \right| = 4\). ...

INTEGER+4 / -02020

10Vector Algebra

Let x0 be the point of Local maxima of \(f(x) = \overrightarrow a .\left( {\overrightarrow b \times \overrightarrow c } \right)\), where \(\overrightarrow a = x\widehat i - 2\widehat j + 3\widehat k\), $$\overrightarrow b = - 2\widehat ...

11Vector Algebra

If \(\overrightarrow a = 2\widehat i + \widehat j + 2\widehat k\), then the value of
$${\left| {\widehat i \times \left( {\overrightarrow a \times \widehat i} \right)} \right|^2} + {\left| {\widehat j \times \left( {\overrightarrow a \t...

INTEGER+4 / -02020

12Vector Algebra

The lines
\(\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)\) and
$$\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} ...

13Vector Algebra

Let a, b c \(\in\) R be such that a2
+ b2
+ c2
= 1. If \(a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)\),
where
\({\theta = {\pi \over 9}}\), then the angle be...

14Vector Algebra

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors such that
\({\left| {\overrightarrow a - \overrightarrow b } \right|^2}\) + $${\left| {\overrightarrow a - \overrightarrow c } \right|^2}$...

INTEGER+4 / -02020

15Vector Algebra

Let the position vectors of points 'A' and 'B' be
\(\widehat i + \widehat j + \widehat k\) and \(2\widehat i + \widehat j + 3\widehat k\), respectively. A point
'P' divides the line segment AB internally in the
ratio
\(\lambda\) : 1 (
$$\l...

INTEGER+4 / -02020

16Vector Algebra

Let \(\overrightarrow a\) = \(\widehat i - \widehat j\), \(\overrightarrow b\) = \(\widehat i + \widehat j + \widehat k\) and \(\overrightarrow c\)
be a vector such that \(\overrightarrow a\) × \(\overrightarrow c\) + $$\overrightarro...

17Vector Algebra

Let \(\overrightarrow a = \widehat i + \widehat j + \sqrt 2 \widehat k,\) \(\overrightarrow b = {b_1}\widehat i + {b_2}\widehat j + \sqrt 2 \widehat k\), \(\overrightarrow c = 5\widehat i + \widehat j + \sqrt 2 \widehat k\) be th...

18Vector Algebra

Let \(\overrightarrow \alpha = 3\widehat i + \widehat j\) and \(\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k\)
. If \(\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}}\),
where $${\...

19Vector Algebra

If a unit vector \(\overrightarrow a\) makes angles \(\pi\)/3 with \(\widehat i\) , \(\pi\)/ 4
with \(\widehat j\) and \(\theta\)\(\in\)(0, \(\pi\)) with \(\widehat k\), then a value of \(\theta\)
is :-

20Vector Algebra

Let \(\mathop a\limits^ \to = 3\mathop i\limits^ \wedge + 2\mathop j\limits^ \wedge + x\mathop k\limits^ \wedge\) and \(\mathop b\limits^ \to = \mathop i\limits^ \wedge - \mathop j\limits^ \wedge + \mathop k\limits^ \wedge\)...

21Vector Algebra

The sum of the distinct real values of \(\mu\), for which the vectors, \(\mu \widehat i + \widehat j + \widehat k,\) \(\widehat i + \mu \widehat j + \widehat k,\) \(\widehat i + \widehat j + \mu \widehat k\) are co-planar, is :

22Vector Algebra

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors, out of which vectors \(\overrightarrow b\) and \(\overrightarrow c\) are non-parallel. If \(\alpha\) and \(\beta\) are the angles whic...

23Vector Algebra

Let \(\overrightarrow a = 3\widehat i + 2\widehat j + 2\widehat k\) and \(\overrightarrow b = \widehat i + 2\widehat j - 2\widehat k\) be two vectors. If a vector perpendicular to both the vectors
$$\overrightarrow a + \overrightarrow b ...

24Vector Algebra

If the volume of parallelopiped formed by the vectors \(\widehat i + \lambda \widehat j + \widehat k\), \(\widehat j + \lambda \widehat k\) and \(\lambda \widehat i + \widehat k\) is minimum, then \(\lambda\) is
equal to :

25Vector Algebra

Let \(\alpha\) \(\in\) R and the three vectors \(\overrightarrow a = \alpha \widehat i + \widehat j + 3\widehat k\), \(\overrightarrow b = 2\widehat i + \widehat j - \alpha \widehat k\) and $$\overrightarrow c = \alpha \widehat i - 2\...

26Vector Algebra

Let \(\overrightarrow a = \widehat i + 2\widehat j + 4\widehat k,\) \(\overrightarrow b = \widehat i + \lambda \widehat j + 4\widehat k\) and $$\overrightarrow c = 2\widehat i + 4\widehat j + \left( {{\lambda ^2} - 1} \right)\widehat k$...

27Vector Algebra

Let \(\sqrt 3 \widehat i + \widehat j,\) \(\widehat i + \sqrt 3 \widehat j\) and \(\beta \widehat i + \left( {1 - \beta } \right)\widehat j\) respectively be the position vectors of the points A, B and C with respect to the origin O. ...

28Vector Algebra

Let \(\overrightarrow a = 2\widehat i + {\lambda _1}\widehat j + 3\widehat k,\,\,\) \(\overrightarrow b = 4\widehat i + \left( {3 - {\lambda _2}} \right)\widehat j + 6\widehat k,\) and $$\overrightarrow c = 3\widehat i + 6\widehat j ...

29Vector Algebra

If \(\overrightarrow \alpha\) = \(\left( {\lambda - 2} \right)\overrightarrow a + \overrightarrow b\) and \(\overrightarrow \beta = \left( {4\lambda - 2} \right)\overrightarrow a + 3\overrightarrow b\) be two given vectors $$\ov...

30Vector Algebra

Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G
divides BM in the ratio, 2 : 1, then cos (\(\angle\)GOA) (O being the origin) is equal to :

31Vector Algebra

The distance of the point having position vector \(- \widehat i + 2\widehat j + 6\widehat k\)
from the straight line passing through the point
(2, 3, – 4) and parallel to the vector, \(6\widehat i + 3\widehat j - 4\widehat k\) is :

32Vector Algebra

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow c = \widehat j - \widehat k\) and a vector \(\overrightarrow b\) be such that \(\overrightarrow a \times \overrightarrow b = \overrightarrow c\) and $$\ove...

33Vector Algebra

If \(\overrightarrow a ,\,\,\overrightarrow b ,\) and \(\overrightarrow C\) are unit vectors such that \(\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,\) then $$\left| {\overrightarrow a \times \over...

34Vector Algebra

If the position vectors of the vertices A, B and C of a \(\Delta\) ABC are respectively \(4\widehat i + 7\widehat j + 8\widehat k,\) \(2\widehat i + 3\widehat j + 4\widehat k,\) and \(2\widehat i + 5\widehat j + 7\widehat k,\) then the ...

35Vector Algebra

Let \(\overrightarrow u\) be a vector coplanar with the vectors \(\overrightarrow a = 2\widehat i + 3\widehat j - \widehat k\) and \(\overrightarrow b = \widehat j + \widehat k\). If \(\overrightarrow u\) is perpendicular to $$\overrigh...

36Vector Algebra

If the vector \(\overrightarrow b = 3\widehat j + 4\widehat k\) is written as the
sum of a vector \(\overrightarrow {{b_1}} ,\) paralel to \(\overrightarrow a = \widehat i + \widehat j\) and a vector \(\overrightarrow {{b_2}} ,\) perpe...

37Vector Algebra

The area (in sq. units) of the parallelogram whose diagonals are along the vectors \(8\widehat i - 6\widehat j\) and \(3\widehat i + 4\widehat j - 12\widehat k,\) is :

38Vector Algebra

Let \(\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k\) and \(\overrightarrow b = \widehat i + \widehat j\).
Let \(\overrightarrow c\) be a vector such that \(\left| {\overrightarrow c - \overrightarrow a } \right| = 3\),
$$\...