Cross Product

Just a quick question about cross products in vectors.

Relating to an equation, how to you determine the order of the elements of the equation? i.e. Torque = r x F, why wouldn't it be written as F x r? Because performing a cross product on r x F will yield a different direction for the torque vector than F x r. I don't know if I'm making much sense in this question. But is there some kind of a convention where you put the position vector first in a cross product (not just talking about torque) or is it different for different equations etc.

Thanks for any answers and I hope my question made some sense.

Michael Collins

It will depend on the particular equation alright. The reason the position vector comes first in the torque equation is because we generally use a right-handed coordinate system, so it should follow the right-hand screw rule.

So, for example, when a ratchet is moving in the clockwise direction (looking from above) due to a force (acting tangential to the direction at all points), the torque is defined to be acting straight downwards from the axis on which it is spinning (this is the right-hand screw rule). So for this to come out of the cross product, the position vector must come first...

Michael Collins

Michael Collins wrote: »

It will depend on the particular equation alright. The reason the position vector comes first in the torque equation is because we generally use a right-handed coordinate system, so it should follow the right-hand screw rule.

So, for example, when a ratchet is moving in the clockwise direction (looking from above) due to a force (acting tangential to the direction at all points), the torque is defined to be acting straight downwards from the axis on which it is spinning (this is the right-hand screw rule). So for this to come out of the cross product, the position vector must come first...

Oh right, ok, I get why it's defined that way (I just remembered about the cork screw rule as I learned it: where X cross Y = Z [where z is vertical, y is horizontal and x is the axis perpendicular to our line of sight] would that be right?). But basically I was just wondering, in general, is there a convention for knowing a specific order for writing equations? It just varies with different equations? Is it that they have to be written in a certain way to satisfy the right hand screw rule?

I think I'm gone beyond the point of making sense, but I appreciate your answer anyway!