We're going to do a couple more examples of finding vector cross product.
Suppose that I give you these two vectors a and B, which both lie in the
plane of, look its my hands, which both lie in the plane of the page.
Ok, so there are a and B. You want to find the direction of a cross B. To find
the magnitude you do a times B times the sine of the angle between them, but we
just want to find the direction right now,
and to do this we're going to use the right hand rule, but first we can use a
little bit of logic.
So, first of all logic says this, whatever the direction of a cross B is which
let's call that c, a cross b the we'll call that c. It has to be perpendicular
to both a and B or perpendicular to the plane of the page.
Well there are only two directions that that could be, right. What that means is
that c either must point straight out of the page or it must point straight into the
page. And, to figure out which one of those two directions it is, what we're
going to have to do is we're gonna have to put our fingers along a. So there are
two ways to do that.
You can either put your fingers along a this way, or you could put your fingers
along a this way, and you have to do it in the way that will let you swing a
down into b like it was a little hinge. So, if you try that notice if you do it
this way,
yeah it's the wrong way right. You'd have to swing all the way the long way around.
If you want to just simply fold a into b the way to do that is to put your
fingers this way then you can curl them down this way.
Notice when you do that your thumb is pointing into the page, so therefore, the
answer is that c is into the page...
and actually I got marker on my wall. Actually, the way we represent
that is that's represented into the page is represented by a little X with a
circle around it. You're supposed to think of it like the tail feathers of an arrow that's
pointing into the page.