Question

Is it possible to add a scalar to a vector? Why or why not?

Answer 1

We cannot add a vector and a scalar quantities together because they have different dimensions.

Explanation:

1. A vector quantity is defined as a physical quantity which has both magnitude and direction. For example, velocity, displacement etc. A scalar quantity is a quantity which has magnitude only but no direction. For example, distance, speed etc.

2. It is impossible to add the two together because of their different dimensions . This basically means that being a vector quantity a particular physical quantity will have both magnitude and direction. Summing the two quantities together we have to describe the direction of the resultant quantity. As a scalar quantity does not have a direction it would be next to impossible to describe the direction of the resultant.

3. For example, let's take a body moving with a velocity of $60km{s}^{-1}$ north and covering a distance of $120km$.

Now, adding the two is not possible as we cannot describe the direction of the resultant quantity.