# Vector proof (cross product)

• Jbreezy

## Homework Statement

If x + v = u
Prove x x v = u x v = x x u

## The Attempt at a Solution

I don't even know where to start with this. I thought that magnitude of the resultant vector would have to be equal. So I started messing with each to see if I could find a pattern.

x x v = | x|| v| sin θ

This is a crap approach I can't find anything. Please give me a hint not the answer. I just can't seem to draw the information in my text together to give myself enough to show this. Thank you.

Just use your definition of u in the equations, and simplify with known properties of the cross product.
It does not help to consider the magnitude of the vectors, as their "direction" has to fit, too.

Hi Jbreezy!

Are you allowed to use the associative rule, a x (b + c) = a x b + a x c ?

Or do you have to use coordinates?

I guess you are allowed to use whatever. I don't understand this problem at all.

ok, then what is x x (u - v) ?

0 vector? This is not anywhere in my eq. though. In terms of the original.

This was a good problem to make me feel like a monkey with a stick.

so, If x + v = u
Prove x x v = u x v = x x u

Sub in u.

x x v = (x + v ) x v = x x(x + v)

So when you distribute.

X x V = X x V + V x V = X x X + X x v

So, V x V = 0 , X x X = 0
So
X x V = X x V = X x V
Thanks

Hi Jbreezy!

(just got up :zzz:)

Yes, that's correct.

But it's a bit long-winded …

you could have done x x v = (x + v ) x v (because v x v = 0)

= u x v,​

or x x v - u x v = … (you finish it )