Vector Algebra PYQs - Last 5 Years

MHT CET / Physics / Mechanics / 27 recent questions

PhysicsMechanics2022-2026

All Vector Algebra PYQs Last 10 Years Create chapter test

Practice 27 MHT CET Physics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

27

PYQs on Page

Physics / Mechanics

2025-2026

Year Range

Based on indexed question metadata

27

Last 5 Years

2022-2026

27

Last 10 Years

2017-2026

Recent Year Trend

2025

2026

202515 max PYQs/year2026

Question Types

27PYQs

MCQ100%

Difficulty Mix

#1 Unknown27

27 in last 5 years27 in last 10 years

Last 5 Years Vector Algebra Questions

Showing 27 of 27 filtered questions.

1Vector Algebra

A boat crosses a river from one bank A to another bank B which is opposite. The distance between them is D. The speed of water is $V_W$ and that of boat relative to water is $V_B$. If $V_B = 2V_W$, the time taken by the boat to cross the ri...

2Vector Algebra

The area of parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

3Vector Algebra

If two vectors $\vec{A} = 4\hat{i} + n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} + 2\hat{j} - \hat{k}$ are mutually perpendicular to each other then value of 'n' is

4Vector Algebra

For two vectors $\vec{P}$ and $\vec{Q}$, $\vec{P} \cdot \vec{Q} = |\vec{P} \times \vec{Q}|$The magnitude of $\vec{R} = \vec{P} + \vec{Q}$ is ($\cos 45^\circ = \dfrac{1}{\sqrt{2}}$) ?

5Vector Algebra

The angle made by vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with x-axis and that with y-axis are respectively.

6Vector Algebra

If a unit vector is represented by $\vec{U} = 0.9\,\hat{i} - 0.2\,\hat{j} + m\hat{k}$, then the value of m is

7Vector Algebra

Resultant of two vectors $\vec{P}$ and $\vec{Q}$ is of magnitude A. If $\vec{Q}$ is reversed, then the resultant is of magnitude B. The value of $A^2 + B^2$ is

8Vector Algebra

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of 'p' is

9Vector Algebra

Let $\vec{P} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{Q} = -(\hat{i} + \hat{j} + \hat{k})$. The angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is

10Vector Algebra

Vectors $a\hat{i} + b\hat{j} + \hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ are perpendicular to each other when $3a + 2b = 7$, the ratio of a to b is $x/2$. The value of x is

11Vector Algebra

A vector $\vec{A}$ when added to the sum of the vectors $(\hat{i} - 2\hat{j} + 2\hat{k})$ and $(-2\hat{i} + \hat{j} - \hat{k})$ gives a unit vector along Y axis. The magnitude of vector $\vec{A}$ is

12Vector Algebra

Let $\vec{A}$ and $\vec{B}$ are two non-zero vectors of different magnitude. Which one of the following is the correct equation ?

13Vector Algebra

The vector sum of the two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence forces $\vec{A}$ and $\vec{B}$ are

14Vector Algebra

Calculate the values of $a$ and $b$ if vectors $a\hat{i} + b\hat{j} = \hat{n}$ and $(\hat{i} + \hat{j})$ are perpendicular to each other

15Vector Algebra

The vectors $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular to each other. This is possible under the condition

16Vector Algebra

Two vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other. When $3 \mathrm{a}+2 \mathrm{~b}=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is

17Vector Algebra

$$ \begin{aligned} & \text { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \\ & |\vec{a} \times \vec{b}|=35 \text {, find } \vec{a} \cdot \vec{b} \end{aligned} $$

18Vector Algebra

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence forces $\vec{A}$ and $\vec{B}$ are

19Vector Algebra

Vector $\vec{A}$ of magnitude $5 \sqrt{3}$ units, another vector $\vec{B}$ of magnitude of 10 units are inclined to each other at an angle of $30^{\circ}$. The magnitude of vector product of the two vectors is $\left[\sin 30^{\circ}=\frac{1...

20Vector Algebra

If $\vec{P}=b \hat{i}+6 \hat{j}+\hat{k} \quad$ and $\quad \vec{Q}=\hat{i}-a \hat{j}+4 \hat{k} \quad$ are perpendicular to each other, also $3 \mathrm{~b}-\mathrm{a}=5$. The value of $a$ and $b$ is

21Vector Algebra

Given $\quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

22Vector Algebra

Given $\quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

23Vector Algebra

The three vector $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 k$ and $\vec{C}=2 \hat{i}-\hat{j}+4 \hat{k}$ will form

24Vector Algebra

A unit vector in the direction of resultant vector of $\vec{A}=-2 \hat{i}+3 \hat{j}+\hat{k}$ and $\vec{B}=\hat{i}+2 \hat{j}-4 \hat{k}$ is

25Vector Algebra

If $\vec{A}=\hat{i}+\hat{j}+3 \hat{k}, \vec{B}=-\hat{i}+\hat{j}+4 \hat{k}$ and $\vec{C}=2 \hat{i}-2 \hat{j}-8 \hat{k}$, then the angle between the vectors $\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}+...

26Vector Algebra

Three vectors are expressed as $\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}$ and $\vec{c}=-\hat{k}$. The unit vector along the direction of sum of these vectors is

27Vector Algebra

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$, then the magnitude of $\overrightarrow{\mathrm{C}}$ is