We've learned how to add vectors, so it now becomes an issue to learn to multiply them. But the many questions arrise about exactly how to perform such a multiplication.
For the Dot product, the following general properties apply:
Part of the Motivation for using the dot product is the physical situation to which it applies, namely that of computin work done on an object by a given force over a given distance, as shown below:
To help us compute this, we define the dot product as follows:
Dot products can also be used to help find the equation for a line in 2 dimentional space. Given the line below, with the indicated normal vector N, we can compute it's equation using the knowledge that the dot product of two perpindicular vectors is 0.