Question

Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not.

Short answer

It is not possible to add a vector and scalar quantity together because they have different dimensions.

Step-by-step solution

Step 1. Given information

We need to write is it possible to add a scalar to a vector. If so, we need to demonstrate. If not we need to explain why not.

Step 2. Explanation

A vector quantity is defined as a physical quantity that has both magnitude and direction. For example velocity, and displacement. A scalar quantity is a quantity that has only magnitude but no direction. For example distance, and speed. It is impossible to add these 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. Summary of 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.

For example, let's take a body moving with a velocity of$60km/s$north and covering a distance of$120km.$Now adding these two are impossible as we cannot describe the direction of the resultant quantity.