Classify the following measures as scalars and vectors.
(i)10kg
(ii)2metres north-west
(iii)40°
(iv)40watt
(v)10-19coulomb
(vi)20m/s2
Classify the following measures as scalars and vectors.
(i)10kg
(ii)2metres north-west
(iii)40°
(iv)40watt
(v)10-19coulomb
(vi)20m/s2
Solution and Explanation
(i)10kg is a scalar quantity because it involves only magnitude.
(ii) 2 meters north-west is a vector quantity as it involves both magnitude and direction.
(iii)40°is a scalar quantity as it involves only magnitude.
(iv)40 watts is a scalar quantity as it involves only magnitude.
(v)10-19 coulomb is a scalar quantity as it involves only magnitude.
(vi)20m/s2 is a vector quantity as it involves magnitude as well as direction.
Top Questions on Vector Algebra
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Mathematics
- Vector Algebra
- Find the shortest distance between the lines: \[ \mathbf{r}_1 = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda (\hat{i} - 2\hat{j} + 3\hat{k}) \] \[ \mathbf{r}_2 = (\hat{i} + 4\hat{k}) + \mu (3\hat{i} - 6\hat{j} + 9\hat{k}) \]
- CBSE CLASS XII - 2025
- Mathematics
- Vector Algebra
- Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
- BITSAT - 2025
- Mathematics
- Vector Algebra
- Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
- BITSAT - 2025
- Mathematics
- Vector Algebra
- The angle between vectors $ \mathbf{a} = \hat{i} + \hat{j} - 2\hat{k} $ and $ \mathbf{b} = 3\hat{i} - \hat{j} + 2\hat{k} $ is:
- CUET (UG) - 2025
- Mathematics
- Vector Algebra
Questions Asked in CBSE CLASS XII exam
Rupal, Shanu and Trisha were partners in a firm sharing profits and losses in the ratio of 4:3:1. Their Balance Sheet as at 31st March, 2024 was as follows:
(i) Trisha's share of profit was entirely taken by Shanu.
(ii) Fixed assets were found to be undervalued by Rs 2,40,000.
(iii) Stock was revalued at Rs 2,00,000.
(iv) Goodwill of the firm was valued at Rs 8,00,000 on Trisha's retirement.
(v) The total capital of the new firm was fixed at Rs 16,00,000 which was adjusted according to the new profit sharing ratio of the partners. For this necessary cash was paid off or brought in by the partners as the case may be.
Prepare Revaluation Account and Partners' Capital Accounts.- CBSE CLASS XII - 2025
- Partnership Accounts
- Explain giving three reasons why tropics show greatest levels of species diversity.
- CBSE CLASS XII - 2025
- Biodiversity
- The element of dilemma, between humanity and patriotism, elevates the character of Dr. Sadao in ‘The Enemy’. Support your answer with evidence from the text.
- CBSE CLASS XII - 2025
- Literature
- Find: \[ \frac{dy}{dx}, \quad \text{if} \quad y = x \tan x + \frac{\sqrt{x^2 + 1}}{2} \]
- CBSE CLASS XII - 2025
- Differentiation
- Solve for \( x \), \[ 2 \tan^{-1} x + \sin^{-1} \left( \frac{2x}{1 + x^2} \right) = 4\sqrt{3} \]
- CBSE CLASS XII - 2025
- Trigonometric Functions
Concepts Used:
Types of Vectors
In general, vectors are used in Maths and Science and are categorized into 10 different types of vectors such as:-
- Unit Vector - When a vector has a magnitude of 1 unit length, called a Unit Vector.
- Co-Initial Vector - Two or more vectors that have the same initial point are known to be Co-Initial Vectors.
- Coplanar Vector - Vectors that lie either in the same plane or are parallel to the same plane are called Coplanar vectors.
- Equal Vector - When two vectors have equal direction as well as magnitude, they are Equal Vectors, even if the initial point is different for both vectors.
- Negative of a Vector - When two vectors have the same magnitude but have exactly different directions.
- Zero Vector - When a vector has the same starting and ending point and has zero magnitudes is called a zero vector. The starting point needs to coincide with the terminal point. It is denoted by 0. It is also known as the null vector.
- Position Vector - A vector that indicates the location or the position of a point in a plane (three-dimensional Cartesian system) w.r.t. its origin. If A is a reference origin and there’s an arbitrary point B in the plane then AB will be called the position vector of the point.
- Like and Unlike Vectors - Like vectors are the vectors that have the same direction. And unlike vectors are the vectors that have opposite directions.
- Collinear Vector - Vectors either lying in the same line or which are parallel to the same line are Collinear vectors.
- Displacement Vector - The vector AB will be known as a displacement vector if a point is displaced from position B to position A.