Vector Algebra PYQs - Last 10 Years
JEE Main / Physics / Mechanics / 38 recent questions
PhysicsMechanics2017-2026
Practice 38 JEE Main Physics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
38
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Physics / Mechanics
2018-2026
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Based on indexed question metadata
20
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2022-2026
38
Last 10 Years
2017-2026
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38PYQs
MCQ65.8%
INTEGER34.2%
Difficulty Mix
#1 Easy22
#2 Medium16
20 in last 5 years38 in last 10 years
Last 10 Years Vector Algebra Questions
Showing 38 of 38 filtered questions.
1Vector Algebra
The velocity of a particle is given as $\vec{v} = -x \hat{i} + 2y \hat{j} - z \hat{k}$ m/s. The magnitude of acceleration at point (1, 2, 4) is ________ m/s2.
MCQ+4 / -12026
2Vector Algebra
Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}$ and $\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}$, respectively. If both the vectors are at righ...
INTEGER+4 / -12025
3Vector Algebra
If \(\vec{a}\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5}{9}\right)\) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(\mathrm{n}\) is _________.
INTEGER+4 / -12024
4Vector Algebra
The resultant of two vectors \(\vec{A}\) and \(\vec{B}\) is perpendicular to \(\vec{A}\) and its magnitude is half that of \(\vec{B}\). The angle between vectors \(\vec{A}\) and \(\vec{B}\) is _________\(^\circ\).
INTEGER+4 / -12024
5Vector Algebra
Three vectors \(\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}\) and \(\overrightarrow{\mathrm{OR}}\) each of magnitude \(\mathrm{A}\) are acting as shown in figure. The resultant of the three vectors is \(\mathrm{A} \sqrt{x}\)....
INTEGER+4 / -12024
6Vector Algebra
For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\vec{A} \cdot(\vec{B} \times \vec{C})=0\), then value of \(x\) is ________.
INTEGER+4 / -12024
7Vector Algebra
The angle between vector \(\vec{Q}\) and the resultant of \((2 \vec{Q}+2 \vec{P})\) and \((2 \vec{Q}-2 \vec{P})\) is :
MCQ+4 / -12024
8Vector Algebra
If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(R\) are inclined at angle \(\theta\), then
MCQ+4 / -12024
9Vector Algebra
A vector has magnitude same as that of \(\vec{A}=3 \hat{i}+4 \hat{j}\) and is parallel to \(\vec{B}=4 \hat{i}+3 \hat{j}\). The \(x\) and \(y\) components of this vector in first quadrant are \(x\) and 3 respectively where \(x=\) _________.
INTEGER+4 / -12024
10Vector Algebra
Two forces having magnitude \(A\) and \(\frac{A}{2}\) are perpendicular to each other. The magnitude of their resultant is:
MCQ+4 / -12023
11Vector Algebra
If \(\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k\) and \(\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k\) then, the unit vector in the direction of $$\overrightarrow P \times \overrightarrow Q...
INTEGER+4 / -12023
12Vector Algebra
Vectors \(a\widehat i + b\widehat j + \widehat k\) and \(2\widehat i - 3\widehat j + 4\widehat k\) are perpendicular to each other when \(3a + 2b = 7\), the ratio of \(a\) to \(b\) is \({x \over 2}\). The value of \(x\) is ____________.
INTEGER+4 / -12023
13Vector Algebra
If two vectors \(\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k\) and \(\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k\) are perpendicular to each other. Then, the value of m will be :
MCQ+4 / -12023
14Vector Algebra
A vector in $x-y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $\mathrm{y}$-component of vector is $2 \sqrt{3}$. The magnitude of $x$-component of the vector will be :
MCQ+4 / -12023
15Vector Algebra
When vector \(\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}\) is subtracted from vector \(\overrightarrow{\mathrm{B}}\), it gives a vector
equal to \(2 \hat{j}\). Then the magnitude of vector \(\overrightarrow{\mathrm{B}}\) will be :
equal to \(2 \hat{j}\). Then the magnitude of vector \(\overrightarrow{\mathrm{B}}\) will be :
MCQ+4 / -12023
16Vector Algebra
Two vectors \(\overrightarrow A\) and \(\overrightarrow B\) have equal magnitudes. If magnitude of \(\overrightarrow A\) + \(\overrightarrow B\) is equal to two times the magnitude of \(\overrightarrow A\) \(-\) \(\overrightarrow B\),...
MCQ+4 / -12022
17Vector Algebra
If the projection of \(2 \hat{i}+4 \hat{j}-2 \hat{k}\) on \(\hat{i}+2 \hat{j}+\alpha \hat{k}\) is zero. Then, the value of \(\alpha\) will be ___________.
INTEGER+4 / -12022
18Vector Algebra
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 ____________ \(\mathrm{m}\).
INTEGER+4 / -12022
19Vector Algebra
Which of the following relations is true for two unit vector \(\widehat A\) and \(\widehat B\) making an angle \(\theta\) to each other?
MCQ+4 / -12022
20Vector Algebra
\(\overrightarrow A\) is a vector quantity such that \(|\overrightarrow A |\) = non-zero constant. Which of the following expression is true for \(\overrightarrow A\) ?
MCQ+4 / -12022
21Vector Algebra
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 ...
MCQ+4 / -12021
22Vector Algebra
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 $$\overrighta...
MCQ+4 / -12021
23Vector Algebra
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 $$\wid...
MCQ+4 / -12021
24Vector Algebra
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} $...
MCQ+4 / -12021
25Vector Algebra
The angle between vector \(\left( {\overrightarrow A } \right)\) and \(\left( {\overrightarrow A - \overrightarrow B } \right)\) is :
MCQ+4 / -12021
26Vector Algebra
Match List - I with List - IIChoose the correct answer from the options given below :
MCQ+4 / -12021
27Vector Algebra
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 an...
MCQ+4 / -12021
28Vector Algebra
In an octagon ABCDEFGH of equal side, what is the sum of \(\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH}\),if, $$\overri...
MCQ+4 / -12021
29Vector Algebra
If \(\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P\), the angle between \(\overrightarrow P\) and \(\overrightarrow Q\) is \(\theta\)(0\(^\circ\) < \(\theta\) < 360\(^\circ\)). The value of '$...
INTEGER+4 / -12021
30Vector Algebra
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 ...
INTEGER+4 / -12021
31Vector Algebra
What will be the projection of vector \(\overrightarrow A = \widehat i + \widehat j + \widehat k\) on vector \(\overrightarrow B = \widehat i + \widehat j\) ?
MCQ+4 / -12021
32Vector Algebra
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| {\o...
MCQ+4 / -12021
33Vector Algebra
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...
MCQ+4 / -12021
34Vector Algebra
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
resul...
and \(\overrightarrow Q\)
is \(\overrightarrow R\)
such that \(\left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right|\)
. The angle \(\theta\) (in degrees) that the
resul...
INTEGER+4 / -02020
35Vector Algebra
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 $$\left( {2\mathop ...
value of $$\left( {2\mathop ...
MCQ+4 / -12019
36Vector Algebra
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 -
MCQ+4 / -12019
37Vector Algebra
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...
MCQ+4 / -12019
38Vector Algebra
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 .\ove...
MCQ+4 / -12018