A) |a| = magnitude = length of the vector.
To find the magnitude use the formula: where n is the number of coordinates you have (in this case 3).
B) Fairly simple: Scalars distribute through vectors like they do through parenthesis, then you just add the corresponding coordinates.
C) This is called the dot product: n being the number of coordinates you have, in this case 3 again. The result of the dot product should always be a scalar.
D) The formula: can be used where is the angle between the vectors.
E) This is known as the cross product. It is only defined (that I know off) in three dimensional space . Check out Cross product - Wikipedia, the free encyclopedia and look under computing the cross prodcut. They explain it better than I can.
F) Is there more information about this one? I myself am not exactly sure what is defined by comp() or sub(). Maybe compliment? Not sure.
And this looks like Calc 3 by the way, but maybe his Calc 2 overlaps into Calc 3? Not sure .