# Another vector proof

1. Oct 20, 2012

### Bipolarity

1. The problem statement, all variables and given/known data
Show that $(u \times (v+w))\cdot r = (u \cdot w)(v \cdot r) - (u \cdot v)(w \cdot r)$

2. Relevant equations

3. The attempt at a solution
So far I have been able to simplify the LHS to:
$(r \times u)\cdot v + (r \times u) \cdot w$ but don't know how to proceed from there.

In fact, I don't know if this problem is even solvable using only vector identities, i.e. without having to prove using components.

All help is appreciated!

BiP

2. Oct 20, 2012

### tiny-tim

Hi Bipolarity!

It's a misprint

try $(u \times (v \times w))\cdot r = (u \cdot w)(v \cdot r) - (u \cdot v)(w \cdot r)$

3. Oct 20, 2012

### Bipolarity

Thanks tiny-tim!

BiP