Vector Algebra PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 17 recent questions
MathematicsAlgebra2017-2026
Practice 17 JEE Advanced Mathematics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
17
PYQs on Page
Mathematics / Algebra
2017-2026
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10
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2022-2026
17
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2017-2026
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17PYQs
INTEGER47.1%
MCQ35.3%
MCQM17.6%
Difficulty Mix
#1 Hard9
#2 Medium8
10 in last 5 years17 in last 10 years
Last 10 Years Vector Algebra Questions
Showing 17 of 17 filtered questions.
1Vector Algebra
Let $ \vec{a}, \vec{b} $ be two vectors, and let P, Q and R be the points with position vectors $ \vec{a}, \vec{b} $ and $ \vec{a} + \vec{b} $, respectively, with respect to the origin O. If $ |\vec{a} + \vec{b}| = \sqrt{21} $, $ |\vec{a} -...
MCQ+3 / -12026
2Vector Algebra
For real numbers $\alpha$, $\beta$, $\gamma$, $\delta$ and $\mu$, consider the matrix
$$ M = \begin{bmatrix} \alpha & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \beta & \frac{1}{\sqrt{3}} \\ \gamma & \delta & \mu \end{...
$$ M = \begin{bmatrix} \alpha & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \beta & \frac{1}{\sqrt{3}} \\ \gamma & \delta & \mu \end{...
MCQ+4 / -12026
3Vector Algebra
Consider the vectors
\(\vec{x}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \quad \vec{y}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \quad \text { and } \quad \vec{z}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k}\)
For two distinct positive real numbers $\...
\(\vec{x}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \quad \vec{y}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \quad \text { and } \quad \vec{z}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k}\)
For two distinct positive real numbers $\...
INTEGER+4 / -02025
4Vector Algebra
Let $\vec{w} = \hat{i} + \hat{j} - 2\hat{k}$, and $\vec{u}$ and $\vec{v}$ be two vectors, such that $\vec{u} \times \vec{v} = \vec{w}$ and $\vec{v} \times \vec{w} = \vec{u}$. Let $\alpha, \beta, \gamma$, and $t$ be real numbers such that
$...
$...
MCQ+4 / -12025
5Vector Algebra
For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\vec{0}$ denote the zero vector. Let $P, Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside th...
INTEGER+4 / -02025
6Vector Algebra
Let $\vec{p}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha, \beta$, and $\gamma$, we have
$$ 15 \hat{i}+10 \hat{j}+6 \hat{k}=\alpha(2 \vec{p}+\vec{q})+\beta(\vec{p}-2 \vec{q})+\gamma(\...
$$ 15 \hat{i}+10 \hat{j}+6 \hat{k}=\alpha(2 \vec{p}+\vec{q})+\beta(\vec{p}-2 \vec{q})+\gamma(\...
INTEGER+4 / -02024
7Vector Algebra
Let $\overrightarrow{O P}=\frac{\alpha-1}{\alpha} \hat{i}+\hat{j}+\hat{k}, \overrightarrow{O Q}=\hat{i}+\frac{\beta-1}{\beta} \hat{j}+\hat{k}$ and $\overrightarrow{O R}=\hat{i}+\hat{j}+\frac{1}{2} \hat{k}$ be three vectors, where $\alpha, \...
INTEGER+4 / -02024
8Vector Algebra
Let the position vectors of the points $P, Q, R$ and $S$ be $\vec{a}=\hat{i}+2 \hat{j}-5 \hat{k}, \vec{b}=3 \hat{i}+6 \hat{j}+3 \hat{k}$, $\vec{c}=\frac{17}{5} \hat{i}+\frac{16}{5} \hat{j}+7 \hat{k}$ and $\vec{d}=2 \hat{i}+\hat{j}+\hat{k}$,...
MCQ+3 / -12023
9Vector Algebra
Let $P$ be the plane $\sqrt{3} x+2 y+3 z=16$ and let
$S=\left\{\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}: \alpha^2+\beta^2+\gamma^2=1\right.$ and the distance of $(\alpha, \beta, \gamma)$ from the plane $P$ is $\left.\frac{7}{2}\right\}$....
$S=\left\{\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}: \alpha^2+\beta^2+\gamma^2=1\right.$ and the distance of $(\alpha, \beta, \gamma)$ from the plane $P$ is $\left.\frac{7}{2}\right\}$....
INTEGER+4 / -02023
10Vector Algebra
Let $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let
$$
\begin{aligned}
& \vec{a}=3 \hat{\imath}+\hat{\jmath}-\hat{k} \text {, } \\
& \vec{b}=\hat{\imath}+b_{2} \hat{\jmath}+b_{3}...
$$
\begin{aligned}
& \vec{a}=3 \hat{\imath}+\hat{\jmath}-\hat{k} \text {, } \\
& \vec{b}=\hat{\imath}+b_{2} \hat{\jmath}+b_{3}...
MCQM+4 / -22022
11Vector Algebra
Let O be the origin and \(\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k\) and \(\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k\) and $$\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lamb...
MCQM+4 / -22021
12Vector Algebra
Let \(\overrightarrow u\), \(\overrightarrow v\) and \(\overrightarrow w\) be vectors in three-dimensional space, where \(\overrightarrow u\) and \(\overrightarrow v\) are unit vectors which are not perpendicular to each other and $$\o...
INTEGER+4 / -02021
13Vector Algebra
Let a and b be positive real numbers. Suppose \(PQ = a\widehat i + b\widehat j\) and \(PS = a\widehat i - b\widehat j\) are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of \(w = \widehat i + \widehat j\) alo...
MCQM+4 / -22020
14Vector Algebra
Let \(\overrightarrow a = 2\widehat i + \widehat j - \widehat k\) and \(\overrightarrow b = \widehat i + 2\widehat j + \widehat k\) be two vectors. Consider a vector c = \(\alpha\)\(\overrightarrow a\) + \(\beta\)\(\overrightarrow b\), $$...
INTEGER+3 / -02019
15Vector Algebra
Let a and b be two unit vectors such that a . b = 0. For some x, y\(\in\)R, let \(\overrightarrow c = x\overrightarrow a + y\overrightarrow b + \overrightarrow a \times \overrightarrow b\). If | \(\overrightarrow c\)| = 2 and the ve...
INTEGER+3 / -02018
16Vector Algebra
Let O be the origin and let PQR be an arbitrary triangle. The point S is such that\(\overrightarrow{OP}\) . \(\overrightarrow{OQ}\) + \(\overrightarrow{OR}\) . \(\overrightarrow{OS}\) = \(\overrightarrow{OR}\) . \(\overrightarrow{OP}\) + $$...
MCQ+3 / -12017
17Vector Algebra
|\(\overrightarrow{OX}\) \(\times\) \(\overrightarrow{OY}\)| = ?
MCQ+3 / -02017