Vectors: Overview, Questions, Preparation

The presence of physical quantities such as direction and magnitudes for a vector represents the meaning of vector quantity. Both the values of direction and magnitude have to be present, or the minimum value has to be 1 for the vector. It is the relationship between the magnitude and direction for the complete representation of the physical quantities. 

Vectors can be broadly classified into two types:

1. Polar vectors: The starting point of these vectors as a point of an application is displacement, force. 
2. Axial vectors: the representation of the rotational effect is determined by axial vectors. They act under the rotational axis as torque, angular momentum, angular velocity, etc. 

Scalars require only magnitude and no direction in accordance with the complete representations. Some of the examples of scalars are distance, work, speed, mass, density, etc. they can be added, multiplied, decided, and subtracted by using algebraic formulas and laws.  

Tensors require different values all in different directions of the physical quantities at the same point. Some of the examples of tensors include pressure, stress, conductivity, resistivity, refractive index, density, wave velocity, inertia's moment, etc. 

Additional types of vectors

1. Unit vector – The unit vector has a unit magnitude. In the direction of the vector, A, the unit vector is written as:

 = A / A

it doesn’t include any units and dimensions. It only represents directions. 

1. Zero vectors – as the name clearly states, the magnitude of these types of vectors is zero or null. The direction of zero vectors is not defined. It is simply denoted as 0. 
2. Equal vectors – the magnitude of equal vectors is equal and in the same direction.
3. Negative vectors – they have equal magnitude but, in the direction, opposite to each other. 
4. Co – initial vectors – co-initial vectors have a common starting point.
5. Collinear vectors – the vectors’ magnitudes can be equal or unequal, but they act parallelly.
6. Position vectors – it can be identified as the straight-line distance. The direction can be at any point of the origin is known as a position vector. 

The laws of vectors can be broadly classified into three types:

1. Triangle law of vectors
2. Parallelogram law of vectors
3. Polygon law of vectors

As per the new pattern of 2021, the chapter ‘Kinematics’ holds a weightage of only 3 marks. It consists of one objective type question of 1 mark and one short question of 2 marks.

Example 1: Illustrate an example of the position and displacement of vectors.  

Answer:

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Example 2: Illustrate an example of two unequal vectors but having the same lengths. 

Answer:

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Example 3: Illustrate using an example, the associate law of vector addition.

Answer: