Vector Algebra PYQs - Last 5 Years

JEE Main / Mathematics / Algebra / 161 recent questions

MathematicsAlgebra2022-2026

All Vector Algebra PYQs Last 10 Years Create chapter test

Practice 161 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.

161

PYQs on Page

Mathematics / Algebra

2022-2026

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Based on indexed question metadata

161

Last 5 Years

2022-2026

161

Last 10 Years

2017-2026

Recent Year Trend

2022

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202248 max PYQs/year2026

Question Types

161PYQs

MCQ80.1%

INTEGER19.9%

Difficulty Mix

#1 Medium135

#2 Hard19

#3 Easy7

161 in last 5 years161 in last 10 years

Last 5 Years Vector Algebra Questions

Showing 11 of 161 filtered questions.

1Vector Algebra

Let $\vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k}$ and $\vec{b}=3 \hat{i}-5 \hat{j}+4 \hat{k}$ be two vectors, such that $\vec{a} \times \vec{b}=-\hat{i}+9 \hat{j}+12 \hat{k}$. Then the projection of $\vec{b}-2 \vec{a}$ on $$\vec{b}...

MCQ+4 / -12022

2Vector Algebra

Let $\overrightarrow a$, $\overrightarrow b$, $\overrightarrow c$ be three non-coplanar vectors such that $\overrightarrow a$ $\times$ $\overrightarrow b$ = 4$\overrightarrow c$, $\overrightarrow b$ $\times$ $$\over...

INTEGER+4 / -12022

3Vector Algebra

If $\overrightarrow a \,.\,\overrightarrow b = 1,\,\overrightarrow b \,.\,\overrightarrow c = 2$ and $\overrightarrow c \,.\,\overrightarrow a = 3$, then the value of $$\left[ {\overrightarrow a \times \left( {\overrightarrow b \ti...

MCQ+4 / -12022

4Vector Algebra

Let $\overrightarrow{\mathrm{a}}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ on th...

MCQ+4 / -12022

5Vector Algebra

Let $\theta$ be the angle between the vectors $\overrightarrow a$ and $\overrightarrow b$, where $|\overrightarrow a | = 4,$ $|\overrightarrow b | = 3$ and $\theta \in \left( {{\pi \over 4},{\pi \over 3}} \right)$. Then $${...

INTEGER+4 / -12022

6Vector Algebra

Let $\overrightarrow a = {a_1}\widehat i + {a_2}\widehat j + {a_3}\widehat k$ ${a_i} > 0$, $i = 1,2,3$ be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of $\overrightarrow a$ on...

MCQ+4 / -12022

7Vector Algebra

Let $\overrightarrow b = \widehat i + \widehat j + \lambda \widehat k$, $\lambda$ $\in$ R. If $\overrightarrow a$ is a vector such that $\overrightarrow a \times \overrightarrow b = 13\widehat i - \widehat j - 4\widehat k$ and...

INTEGER+4 / -12022

8Vector Algebra

Let $\mathrm{ABC}$ be a triangle such that $$\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{c}},|\overrightarrow{\ma...

MCQ+4 / -12022

9Vector Algebra

Let $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and let $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$. Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :

MCQ+4 / -12022

10Vector Algebra

Let $\widehat a$, $\widehat b$ be unit vectors. If $\overrightarrow c$ be a vector such that the angle between $\widehat a$ and $\overrightarrow c$ is ${\pi \over {12}}$, and $$\widehat b = \overrightarrow c + 2\left( {\over...

MCQ+4 / -12022

11Vector Algebra

Let $\widehat a$ and $\widehat b$ be two unit vectors such that $|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2$. If $\theta$ $\in$ (0, $\pi$) is the angle between $\widehat a$ and $\widehat b$, then among...

MCQ+4 / -12022