What is the dot product of two vectors?
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.
Another way of calculating the dot product is to use the coordinates of the vectors:
If you have:
you can write:
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.