I teach an AB course, but have two students who are studying the BC material independently (more or less...I help them out when they get really stuck, but they are pretty bright and can read the book and figure out most of the stuff themselves).
Anyhow, one of the ways I assist them is in targeting the material they should work on each week. Today I was reviewing the BC outline and notice that they need to learn vector-valued functions. This topic is not in our text, so I have to supplement the material. Although I've had a couple of other students take the BC exam (one in 1994 and one in 1996), I don't remember supplementing this material for them. Maybe they just lucked out and such questions were not on the exam? Or maybe they knew it because their AP Physics teacher covered that material???
Well, anyway, my question is this...
For derivatives, etc... of vector valued functions, do the students need to be able to do functions with 3 vector components (should they be comfortable with velocity and accel in 3 dimensions?), or are two dimensions enough? Do they need to know dot product, the normal vector (i..e. cross-product)?
Any guidelines or suggestions on how much of the vector material they need to study would be appreciated.