What is the dot product and cross product?

[ƒ(x)]

Not so much an actual problem, more like concepts. What exactly is the dot product? How about the cross product?

 

[Tinyboss]

The dot product tells you roughly how close two vectors are in direction (it's equal to the cosine of the angle between them). Another way to think about it is "projecting" one vector onto another.

The cross product of two vectors in 3-space gives you a third vector, perpendicular to both of the first two, whose length is the area of the parallelogram defined by the first two.

Wikipedia has diagrams.