May 21, 2020


(For all Top Exams) 


Vectors and Scalars 

What are vectors? Vectors are those quantities that have both magnitude and direction. Scalars are those quantities that have ONLY magnitude. 

Let us take two examples to make our concept of vectors totally clear. 

Let us take force and temperature. 

Now suppose there are two or more forces acting on a body. Is it not important IN WHICH DIRECTION they are acting? 

If two equal forces act in exactly opposite directions, the body will not move. 

If they act in the same direction, the body will move with both forces added up. 

The force might act at different angles too. Is it not? 

Definitely, by nature force has both magnitude and direction. Such quantities are called as vectors. 

Other examples of vectors are Velocity, Momentum, Displacement etc. In each of them, the direction becomes important. 

Now, let us take temperature. In any direction, the temperature remains constant. There is nothing like a direction. Such quantities, where direction is not inherent to the quantity and only magnitude is there, we call scalars. 

Other examples of scalar quantities are mass, distance, speed, work, energy..etc 

What is Vector Algebra? 

Now, since vector quantities have both magnitude and direction, how do we ADD or SUM UP or find what is called the RESULTANT of two vectors. 

In real life, suppose we have many forces acting on a body, at different angles, how do we predict beforehand, what the RESULTANT force would be, and hence finally how the body would move? 

It cannot be just addition of magnitudes because DIRECTION also is involved. So, we have concepts of vector algebra and with these concepts, we can add/sum up vector quantities keeping direction in mind also. 

We also have PRODUCTS, dot product and cross product, some special concepts that we will see in the later units. 

To do all these things, we need some simple and clear definitions and symbols that we use in vector algebra. In the next section we will study them.