Calc3.2

Vectors, and Vector Functions

A vector is a mathematical object which has magnitude like a number, but also direction. For example, if I wanted to describe how a person is driving at any particular time, I would need two numbers: their speed, and some measure of their direction (the angle it makes with true north, for example). These two quantities together constitute the motion vector of that person.

We also use vectors to describe position: for example, to locate an object, it suffices to know how far it is from you, and in what direction.

Vectors are the bread and butter of multivariable calculus because they pack multiple variables into a single, easily manipulated quantity. Let's look at some more specific examples.

In our first descriptions, we used a coordinate system you should be familiar with call "polar coordinates." If you aren't familiar with this system, we will review them shortly. When using Cartesian coordinates, vectors are very, very familiar. The point $(x,y)\$ has position vector, or put more simply, is the vector written ${\begin{pmatrix}x\\y\end{pmatrix}}\$

Coordinate Systems

cartesian

polar

brief discussion about cylindrical

spherical