# How do you deal with commas in vector equations

• I
• Josh The Cool

#### Josh The Cool

Hey,
So I've been working on a physics project and I'm trying to understand force. This website has all my answers http://www.myphysicslab.com/collision.html but I don't understand with they use commas. For example (Rx, Ry, 0) × (Tx, Ty, 0) = (0, 0, RxTyRyTx). Now it is dealing with vectors for example F = (Fx, Fy). I think maybe even 3 dimensional victors. But how do I use this? How do I find X? Can someone point me somewhere?

These are vectors and that the ##\times## generally means the vector cross product.

• Josh The Cool
That is what I don't understand, what is a cross product? I'm a computer programmer not a physicist, so thank you for forgiving my lack of knowledge.

EDIT: with F = Fx,Fy if I want to find the values of the vectors, like just Fx, how do I do the math?
EDIT: After you said the cross product thing I googled it and that was what I wanted to know. Thanks mate

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• berkeman
A vector is just a list of numbers. In 3D space you might have (x,y,z) just like some python list or 1D mathematica array. The list index, i.e. position of the number, just implies association with a particular dimension. Like the x, y or z-axis.
Crossproduct is crosswise multiplication of the list elements in a vector
V1 x V2 = ( y1z2 - z1y2, z1x2 - x1z2, x1y2 - y1x2)

Notice the crossproduct of two vectors is also a vector.
The vector elements, e.g. x1, y1 and z1, can be found by resolving the vector, e.g. V1: http://www.everythingmaths.co.za/sc...ons/01-vectors-in-two-dimensions-04.cnxmlplus

It is important to note that the cross product is defined for 3 dimensions, only. It can be generalized (by changing its definition) to other dimensional spaces. Of special note is that it is directional. Two vectors in 3-d have 2 possible vectors perpendicular to them and the usual definition picks one, usually the right-hand rule. I'd also disagree that a vector is "just" an n-tuple of numbers. A vector is usually conceived to be an independent geometrical object, whose components have values (assuming the components are numbers, not functions) which depend on the coordinates chosen. For instance a rock moving with velocity of (1,2,3) and units of mph will have different components if expressed in km/hr, or a point (1,1,1) in space will have different coordinates if a different origin is used. You'll note that "space" has a more general meaning than the one we are used to. (Although both my examples are of things in normal 3-d space) The space of the velocity is 3-d but it is of a velocity space, while position space is what we usually think of as Space. You can have many other spaces, of many other dimensions, one example is the space of the energies of 3 particles. It would also be 3-d, but without obvious relation to our familiar Space. Anyway, context makes clear (to those who understand) what the space under discussion is. Note that abstract vector algebra does treat vector components as ordered sets (lists), so while claiming a vector is a list isn't wrong, it is just one POV and there are others, especially in Physics.

• Complex Root
I'd also disagree that a vector is "just" an n-tuple of numbers.

I didn't mean there was nothing more to it just that, on one level, a vector is a list of values measured along the basis vectors of some reference frame. In fact because the components are not invariant under most coordinate transformation, it is as well to view it as just a list for many applications. The OP was looking for an intro into vectors, I think and he is a computer guy so it seemed appropriate.