The Right-Hand Method (ugh)

[M_LeComte]

I'm learning about cross-products of vectors right now. What I don't get is how the right-hand method of determining the direction of the z-axis (or k, whatever) actually works. I've looked at a couple online explanations and I'm still just as confused. Is there anywhere online that I could download a movie demonstration of this? Is there an alternative to this method even?

(In case you were wondering, I am teaching myself Advanced Physics through a textbook. And I can't ask someone who is knowledgeable about physics to show me because I don't know anyone.)

 

[jamesrc]

Try this:

Let's say your looking for the direction of a cross b

- hold your hand open with your thumb sticking up
- line up your fingers with a so that if you were to close your fingers, you'd be moving towards b (either you keep your hand with your thumb up or you have to turn your hand upside down)
- your thumb is pointing in the direction of the cross product

 

[M_LeComte]

The part I don't get is: "line up your fingers with a so that if you were to close your fingers, you'd be moving towards b"

Do you mean pretend to grasp b? I just don't get how curling my fingers would make my hand move towards b, or anywhere.

 

[jamesrc]

I guess this is tough to explain without a picture. You don't move your hand; you just curl your fingers. I was thinking that your book had the whole forefinger this way middle finger that way explanation which I never liked.

Maybe this one will help:
http://www.math.montana.edu/frankw/ccp/multiworld/twothree/atv/screwrule.htm [Broken]

(he writes the cross product as x^y)
If you curl your fingers so that "x turns toward the vector y in the shortest way" your thumb will be pointing in the direction of the cross product (the direction you are driving the screw).

 

[PhysicsDude55]

One area of physics where the cross product is used a lot is rotational forces, such as torque and centrifugal force.

So, think of a rotating cylinder. Now picture your hand representing the forces of that cylinder.

With your hand uncurled, the tips of your fingers point raially outward, signifying centrifugal force(acceleration). And the underside of your fingers and palm (not curled) represend the instantanious velocity, which is tangent to the outside of the cylinder. And then your thumb represents the axis of rotaion, where posotive (thumb up) signifies counter-clockwise rotation, and negative (thumb down) represents clockwise rotation.

Does that help? Practical examples always helped me understand.

 

[M_LeComte]

Thank you Dude and james, I think I've got it now.