> Could you please tell about vector cross & dot products too, then?  :o)

The dot product is an scalar binary vector space inner product operator.
Don't get scared, that only means that it is a function that takes TWO
VECTORS and gives a NUMBER as a result.

The dot product is very important because it lets you find the angle between
two vectors, see if they are orthogonal (perpendicular), etc.
It is also very important because it lets you project a vector into a
plane... something like finding the "shadow" of a vector in a plane. It lets
you do many things!

If we have two 3d vectors: A=(a1,a2,a3), B=(b1,b2,b3), you can compute it's
dot product in two alternative but equivalent ways:

1) A dot B = a1*b1 + a2*b2 + a3*b3
2) A dot B = |A|*|B|*cos(theta)

where theta is the angle (in radians!) between A and B. And |A| is the
euclidean norm (length) of A defined by

|A|=sqrt(a1^2 + a2^2 + a3^2)

So, if A and B are orthogonal (perpendicular), then cos(theta)=0 and then
the dot product is equal to zero.

Now, the cross product, is a function that takes TWO VECTORS and gives a
VECTOR as a result. The most important characteristic from the cross product
is that the resulting vector is orthogonal to the other two original
vectors. And that's very useful for finding normal vectors, and other
things.

The computation is more cumbersome (although there is a trick to memorize it
using a determinant, but I won't state it):

if A cross B = C = [c1,c2,c3] then

c1 = a2*b3 - a3*b2
c2 = a3*b1 - a1*b3
c3 = a1*b2 - a2*b1

As you can prove easily, the resulting vector C is orthogonal to A and B
(using dot product and a little of algebra)

Well, I hope I made myself clear and help you out of this,

Fernando.

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