# What is the dot product of two vectors?

##### 1 Answer

The **dot product** of two vectors is a quite interesting operation because it gives, as a result, a...SCALAR (a number without vectorial properties)!

As a definition you have:

Given two vectors

i.e. is equal to the product of the modules of the two vectors times de cosine of the angle between them.

For example:

if

Another way of calculating the dot product is to use the coordinates of the vectors:

If you have:

(where

you can write:

For example:

if:

This operation has important practical applications. For example in Physics the dot product of Force (a vector) and displacement (a vector) gives as a result a number without vectorial characteristics, called, **Work**.