Chapter 10. Vectors
Vectors are used to represent a change in location: given any two points \( p_1 \) and \( p_2 \), we can find a vector \( v \) that starts at \( p_1 \) and ends at \( p_2 \).
We can think of vectors as having both a length and a direction. The length, or magnitude, of a vector is the distance between the endpoints. By looking at vectors with magnitude one, we find vectors that fit as rays on the unit circle.
Each such unit vector represents a unique direction. Our goal for this chapter is to show that we can produce any vector \( v \) by scaling a unit vector up or down to the desired length.