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.

- What is the rule?
- What kind of output do you get? (Scalar? Vector? Tensor?)
- Is this multiplication Commuttative?
For the Dot product, the following general properties apply:

**Motivation**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. **N**= a**i**+ b**j**- P0P=(x-x0)
**i**+ (y-y0)**j** **N**dotted with P0P = 0- a(x-x0) + b(y-y0)=0
- ax+by = a*x0 + b*y0 = c.
### Projections

**Vector Projections**- Resolve
**B**into**B1**(parallel to**A**) and**B2**(perpindicular to**A**).