Vector / Scalar Projection

This question has me majorly confused. I've been going quite well so far at Calculus (that's the name of the subject) but this question has me completely stumped. Complete answers aren't necessary since I want to get this done myself (i don't know what the rules are about giving out answers) but I'd really appreciate a couple of prods in the right direction.

Here we go:

Let **u** = (2,1,-3) and **v** = (1,4,2) be vectors in R3. Calculate and draw sketches to explain:

(a) the scalar projection of **u** on **v**

(b) the scalar projection of **v** on **u**

(c) the vector projection of **u** in the direction of **v**

(d) the vector projection of **v** in the direction perpendicular to **u**Okay. I started with (a) and went like this:

scalar projection is **v . u** where **v** is a unit vector.

After calculating that dot product as: (**v** / ||**v**||) . **u**

I was surprised to have it equal to 0, which means that the two vectors are perpendicular. Can somebody explain whether that is correct or not and what it means for solving the rest of the questions?

Thanks :)

Also, how can I include maths symbols in posts?