Now remember we learned that the velocity at a point on the object , where is the distance between the point and the axis. It is the distance measured perpendicularly from the axis to the point. Now lets try to express this relation as a vector relation.

If we define a vector , measuring
the moving point in relation to an origin that is on the axis,
we'd like to say ,
except that makes no sense since we haven't defined how
to multiply to vectors and get a vector! Well it's about
time we do that. So we have a vector pointing up,
and a vector *r* pointing onto some point on the object
as pictured below

in this picture is . is the angle between and . so

What about it's direction. It's not hard to see that
is perpendicular to both *bom* and .

This is what's called a *cross product* or *vector
product*. If you have two vectors and , then
we can define a vector . It has
a magnitude , with being the
angle between and . And it's perpendicular to
both and .

So we see that . Could I have said ? The answer is no! We have to be careful about getting our signs right, and again we use a right hand rule to make that clear.

If the first vector being multiplied, is represented by the stretched fingers, and the second, by the bent ones then the thumb gives the direction of the resulting cross product. Notice that if the order was reversed, so would the directions so that !

Sun Feb 23 15:54:50 PST 1997