Vector Scalar Product and KE questions

[Walczyk]

Just a few questions from this set I have to do, I missed the class on these topics so I'm just a little confused with these last few problems.

http://img161.imageshack.us/img161/2307/problem43eu.png

Concerning sets 38-39, and 40-41, I've grasped how to scalar multiply these vectors, but not how to find the angle it seems, wondering if anybody can check those out. as for the last set, i was able to find the first answer with k=.5*m*v^2, but I'm not sure what the second question is asking. I missed the class on these topics (accelerated physics in the summer, awfully bad to miss a class). thanks in advance!

 

[Maxwell]

I believe the formula you need to use is something like:

cos(theta) = (a * b)/(|a||b|)

Where * is the dot product of a and b.

 

[Walczyk]

aye, i wroked those angles out, inverse cosine.
edit: I've figured out all the problems, thanks for the help everyone.