Vector multiplication with scalars I'm a little confused as to the results of multiplying vectors and scalars. If I multiply a vector and a scalar, is it a vector? And if I multiply a vector and another vector, is the results also a vector? I looked at http://mathworld.wolfram.com/VectorMultiplication.html but still haven't figured it out.
Ok, this is a math question really, but a 'physics answer' could go as follows:

Velocity is a vector: it has a size (speed) and a direction. If you multiply a velocity vector by - say - a factor of two, you go twice as fast in the same direction. So multiplying a (velocity) vector with a scalar gives again a (velocity) vector. 

Now the multiplication of two vectors. There are several meaningful definitions of vector multiplications. Out of these, the inner product multiplication (or dot product) is most abundant in physics. We take force vectors and displacement vectors as examples. Dot multiplying the force vector exerted on a particle with its displacement vector yields the amount of work done. This amount of work is a scalar (a number without further attributes such as direction). So the dot product between two vectors gives a scalar.

As I mentioned, other definitions of products between vectors are possible. For instance, the direct product between two vectors yields a (rank two) tensor. No need to be bothered about this in basic physics though.
God the answers above are mere showing off. Vector multiplied by a scalar is a scalar. vector multiplied by another vector can take two forms, known as scalar product (inner product) or cross product. The former (inner) is a scalar.