3D visualization

Before I get going with the topic of today's post I would like to add another resource I found for understanding the geometry involved in the dot product and cross product. Just follow the links to play.

While it is possible to solve homework questions without having a good handle on the geometry of the functions we are dealing with, I wouldn't advise it.  Here are some 3 dimensional function graphing applets that you can use.  For lines in 3 dimensions it is best to use the parametric equations, making this a good choice:

For graphing planes the following works well(make sure and use a * for multiplication, so 3x=3*x):