Vector Algebra PYQs - Last 5 Years
KCET / Mathematics / Algebra / 17 recent questions
MathematicsAlgebra2022-2026
Practice 17 KCET Mathematics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Algebra
2022-2026
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2022-2026
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MCQ100%
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17 in last 5 years17 in last 10 years
Last 5 Years Vector Algebra Questions
Showing 17 of 17 filtered questions.
1Vector Algebra
If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to
MCQ+1 / -02026
2Vector Algebra
If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is
MCQ+1 / -02026
3Vector Algebra
The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is
MCQ+1 / -02026
4Vector Algebra
Consider the following statements :
Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$
Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the follo...
Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$
Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the follo...
MCQ+1 / -02025
5Vector Algebra
If $|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{~b}}|=2$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=12$, then the value of $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|$ is
MCQ+1 / -02025
6Vector Algebra
If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is
MCQ+1 / -02025
7Vector Algebra
If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $\mathbf{p}=\frac{\mathbf{a} \times \mathbf{c}}{[\mathbf{a b c}]}, \mathbf{q}=\frac{\mathbf{c} \times \mathbf{a}}{[\mathbf...
MCQ+1 / -02024
8Vector Algebra
Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{b}$ is a unit vector, if
MCQ+1 / -02024
9Vector Algebra
The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ are the sides of a $\triangle A B C$, The length of the median through $A$ is
MCQ+1 / -02024
10Vector Algebra
The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is
MCQ+1 / -02024
11Vector Algebra
The component of \(\hat{\mathbf{i}}\) in the direction of the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) is
MCQ+1 / -02023
12Vector Algebra
If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\), then
MCQ+1 / -02023
13Vector Algebra
If \(\mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0\) and \((\mathbf{a} \times \mathbf{b})+(\mathbf{b} \times \mathbf{c})+(\mathbf{c} \times \mathbf{a})=\lambda(\mathbf{b} \times \mathbf{c})\), then the value of \(\lambda\) is equal to
MCQ+1 / -02023
14Vector Algebra
\(|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144\) and \(|\mathbf{a}|=4\), then \(|\mathbf{b}|\) is equal to
MCQ+1 / -02023
15Vector Algebra
If \(\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\), then express \(\beta\) in the form \(\beta=\beta_1+\beta_2\) where \(\beta_1\) is parallel to \(\alpha\) and \(\beta_2\) is perpe...
MCQ+1 / -02022
16Vector Algebra
If \(|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36\) and \(|\mathbf{a}|=3\), then \(|\mathbf{a}|\) is equal to
MCQ+1 / -02022
17Vector Algebra
If \(|\mathbf{a}|=2\) and \(|\mathbf{b}|=3\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then the length of the vector \(\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|\) is
MCQ+1 / -02022