calculus-based physics for scientists and engineers

Coordinate Systems in 2D and 3D

Two Dimensional Cartesian Coordinate Systems

Remember to imagine coordinate systems as rulers that are placed in a real system where you are trying to measure something. For two dimensions, we need two rulers. Their role is the same: to allow us to represent a real event with numbers that we can then model mathematically.

Cartesian means the different axes of the coordinate system are straight lines that are perpendicular to each other.

Like in 1D, we have choices to make. We choose where to place the origin and the positive directions of the axes. Making good choices can make solving problems easier. How can you make good choices? Practice!

Three Dimensional Cartesian Coordinate Systems

A three dimensional Cartesian coordinate system has a third axis perpendicular to the other two. There are two possibilities, but there is one catch, it can't point any direction you want.

In the video I show you how to figure it out! We learn about right- and left-handed coordinate systems, and have our first experience with right hand rules!


Do Now!   Do these exercises immediately.

Not Now!   Do these after you start to forget the topic, say in a week.

More!   More exercises if you want. Maybe review before a test.

Required Problems

Optional Problems