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Vectors - ISC Class 12 Mathematics Questions with Answers

55 past-paper questions on Vectors from ISC Class 12 Mathematics papers (2026-2017), newest first. Open one to see its answer.

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A scalar is multiplied by a unit vector, then the resultant is: Statement 1: A vector with the magnitude of the scalar. Statement… 2026 · 1 mark · MCQ
A school’s media team identifies three points A, B and C on a large bulletin board to position three charts. The position vectors… 2026 · 2 marks · Numerical
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. Consider… 2026 · 5 marks · Short answer
Find the area of a parallelogram whose adjacent sides are given by the vectors… 2026 · 1 mark · Short answer
If $\vec{a}$ and $\vec{b}$ are mutually perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$, then find the… 2026 · 2 marks · Short answer
Three drone cameras A, B and C are recording a hockey match. Their positions with respect to a control tower O are given by the… 2026 · 2 marks · Derivation
A building is to be constructed in the form of a triangular pyramid ABCD as shown in the figure. Let the angular points be… 2026 · 2 marks · Short answer
What are the values of $x$ for which the angle between the vectors $2x^2\hat{i} + 3x\hat{j} + \hat{k}$ and… 2026 · 2 marks · Short answer
For vector $\vec{a}$, $\vec{a} \cdot \hat{i} = \vec{a} \cdot \hat{j} = \vec{a} \cdot \hat{k}$ and $|\vec{a}| = 300$. Then… 2026 · 1 mark · MCQ
Three forces act simultaneously on a space satellite in such a way that the satellite remains in equilibrium. The forces are… 2026 · 2 marks · Numerical
A unit vector in the direction of the sum of the vectors $2\hat{i} + 3\hat{j} - \hat{k}$ and $4\hat{i} - 3\hat{j} + 2\hat{k}$ is: 2026 · 1 mark · MCQ
For any three vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$, Statement 1: $\vec{a} \cdot (\vec{b} \times \vec{c})$ is a scalar… 2026 · 1 mark · MCQ
The projection of $\hat{\imath} + 2\hat{\jmath} - 3\hat{k}$ on $2\hat{\imath} - \hat{\jmath} + \hat{k}$ is: 2026 · 1 mark · MCQ
If $|\vec{a}| = 1$, $|\vec{b}| = 2$, $|\vec{c}| = 3$ and $\vec{a} + \vec{b} + \vec{c} = 0$, then verify… 2025 · 1 mark · Short answer
Consider the position vectors of $A$, $B$ and $C$ as $\vec{OA} = 2\hat{i} - 2\hat{j} + \hat{k}$… 2025 · 4 marks · Short answer
If $|\vec{a} - \vec{b}| = |\vec{a} + \vec{b}|$ in the given figure, what inference can you draw? 2025 · 2 marks · Short answer
Consider the figure, shown below: Statement 1: The position vector of $P$ is $\frac{2\vec{c} + 3\vec{a}}{5}$ Statement 2: The… 2025 · 1 mark · MCQ
Four students are playing a game. In a box, there are four strips of paper with four expressions written on each one. The student… 2025 · 1 mark · MCQ
$\vec{PQ} \times (\vec{RS} + \vec{ST}) \neq \vec{0}$. The vectors $\vec{PQ}, \vec{QR}, \vec{RS}, \vec{ST}, \vec{TU}$ and… 2025 · 1 mark · Assertion-reason
Consider the two vectors $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = 5\hat{i} + q\hat{j} - \hat{k}$. Calculate… 2025 · 4 marks · Short answer
What are the values of $x$ for which the angle between the vectors $2x^2\hat{i} + 3x\hat{j} + \hat{k}$ and… 2025 · 2 marks · Short answer
Find a vector of magnitude 9 units and perpendicular to the vectors $\vec{a} = 4\hat{i} - \hat{j} + \hat{k}$ and… 2025 · 2 marks · Short answer
Let $\vec{\alpha} = 3\hat{i} + \hat{j}$ and $\vec{\beta} = 2\hat{i} - \hat{j} + 3\hat{k}$. If… 2025 · 4 marks · Long answer
The value of… 2025 · 1 mark · MCQ
If $\vec{p} \times \vec{q} = \vec{0}$ and $\vec{p} \cdot \vec{q} = 0$, then what conclusion can we draw? 2025 · 1 mark · Short answer
$(\vec{a} + \vec{b}) \cdot (\vec{b} - \vec{a}) = 2 (a^2 + b^2)$ 2025 · 1 mark · Assertion-reason
If the angle between $\vec{a} = -3\hat{i} + x\hat{j} + \hat{k}$ and $\vec{b} = x\hat{i} + 2x\hat{j} + \hat{k}$ is acute and the… 2025 · 2 marks · Short answer
Derive a condition for which given, $\vec{b} = \vec{c}$, we can say $\vec{a} \times \vec{b} = \vec{c} \times \vec{a}$? 2025 · 2 marks · Short answer
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. If… 2024 · 5 marks · Short answer
If $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ where $\vec{a}$, $\vec{b}$ and $\vec{c}$ are non-zero vectors, then prove… 2024 · 2 marks · Derivation
If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a} \times \vec{b}| = \vec{a} \cdot \vec{b}$, find the angle… 2024 · 2 marks · Numerical
If the two vectors $3\hat{i} + a\hat{j} + \hat{k}$ and $2\hat{i} - \hat{j} + 8\hat{k}$ are perpendicular to each other, then find… 2023 · 1 mark · Numerical
If $A(1, 2, -3)$ and $B(-1, -2, 1)$ are the end points of a vector $\vec{AB}$ then find the unit vector in the direction of… 2023 · 2 marks · Short answer
For any two non-zero vectors $\vec{a}$ and $\vec{b}$, if $|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|$, then find the… 2023 · 2 marks · Short answer
Find the area of the parallelogram whose diagonals are $\hat{i} - 3\hat{j} + \hat{k}$ and $\hat{i} + \hat{j} + \hat{k}$. 2023 · 1 mark · Numerical
If $|\vec{a}| = 3$, $|\vec{b}| = \frac{\sqrt{2}}{3}$ and $\vec{a} \times \vec{b}$ is a unit vector then the angle between… 2023 · 1 mark · MCQ
If $\hat{a}$ is unit vector and $(2\vec{x} - 3\hat{a}) \cdot (2\vec{x} + 3\hat{a}) = 91$, find the value of $|\vec{x}|$. 2023 · 2 marks · Numerical
Find the area of the triangle whose adjacent sides are $\hat{i} + 4\hat{j} - \hat{k}$ and $\hat{i} + \hat{j} + 2\hat{k}$. 2023 · 2 marks · Short answer
The given figure shows an air plant holder which is in the shape of a tetrahedron. Let $A(1, 1, 1)$, $B(2, 1, 3)$, $C(3, 2, 2)$ &… 2022 · 8 marks · Case based
What will be the value of m if the vector $2\hat{i} + m\hat{j} + \hat{k}$ is perpendicular to $2\hat{i} - \hat{j} + 3\hat{k}$? 2022 · 2 marks · MCQ
[5×1] In sub-parts (i) and (ii) choose the correct options and in sub-parts (iii) to (v), answer the questions as instructed. If… 2021 · 5 marks · Short answer
Find $\lambda$ if the scalar projection of $\vec{a} = \lambda\hat{i} + \hat{j} + 4\hat{k}$ on… 2021 · 2 marks · Short answer
If $\vec{a}$ and $\vec{b}$ are perpendicular vectors, $|\vec{a} + \vec{b}| = 13$ and $|\vec{a}| = 5$, find the value of… 2021 · 2 marks · Numerical
Prove that $\vec{a} \cdot [(\vec{b} + \vec{c}) \times (\vec{a} + 3\vec{b} + 4\vec{c})] = [\vec{a} \quad \vec{b} \quad \vec{c}]$. 2020 · 4 marks · Derivation
[3×2] Write a vector of magnitude of 18 units in the direction of the vector $\hat{i} - 2\hat{j} - 2\hat{k}$. Find the angle… 2020 · 6 marks · Short answer
Using vectors, find the area of the triangle whose vertices are… 2020 · 4 marks · Numerical
If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, find the value of $x$ such that the vectors… 2019 · 4 marks · Numerical
If $\vec{a} = -\hat{i} - 2\hat{j} + 3\hat{k}$, $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$, prove that $\vec{a}$ and… 2019 · 4 marks · Derivation
Show that… 2018 · 4 marks · Derivation
Show that: $\vec{a} \cdot (\vec{b} + \vec{c}) \times (\vec{a} + 2\vec{b} + 3\vec{c}) = [\vec{a} \; \vec{b} \; \vec{c}]$ 2018 · 4 marks · Derivation
Show that the four points $A, B, C$ and $D$ with position vectors $4\hat{\imath} + 5\hat{\jmath} + \hat{k}$… 2018 · 4 marks · Derivation
[3×2] Find $\lambda$ if the scalar projection of $\vec{a} = \lambda\hat{\imath} + \hat{\jmath} + 4\hat{k}$ on… 2018 · 6 marks · Short answer
If $A, B, C$ are three non-collinear points with position vectors $\vec{a}, \vec{b}, \vec{c}$, respectively, then show that the… 2018 · 4 marks · Derivation
If $\vec{a}, \vec{b}, \vec{c}$ are three mutually perpendicular vectors of equal magnitude, prove that… 2017 · 5 marks · Short answer
Find the value of $\lambda$ for which the four points with position vectors $6\hat{i} - 7\hat{j}$… 2017 · 5 marks · Numerical

Vectors - ISC Class 12 Mathematics Questions with Answers

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