Is there a vector proof for (u x (v+w)) . r = (u . w)(v . r) - (u . v)(w . r)?

[Bipolarity]

Homework Statement

Show that $(u \times (v+w))\cdot r = (u \cdot w)(v \cdot r) - (u \cdot v)(w \cdot r)$

Homework Equations

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

 

[tiny-tim]

Hi Bipolarity!

It's a misprint …

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

 

[Bipolarity]

Thanks tiny-tim!

BiP