How can prove this ?

1. Apr 24, 2007

jiangxiaoyu

All characters are vector quantities

The question is prove the following equation:

→ → → → → → → → → →
(2a + b)×(c -a ) + (b + c)×(a × b) = a × c

2. Apr 24, 2007

neutrino

Can you put forward any idea that you may have on solving this problem?

3. Apr 24, 2007

AiRAVATA

Why don't you use the asociative, distributive and anticonmutative properties of the cross product?

4. Apr 24, 2007

HallsofIvy

It looks very simple to me by just doing what AiRAVATA says. As you would expect, a loot of things cancel. Look especially carefully at the "anti-commutative" property since you may not be used to that. In particular, what is axa?

5. Apr 24, 2007

jiangxiaoyu

a x a <=> |a|*|a|*cosθ ，
because θ=0 so |a|*|a|*cosθ =0 , a x a =0
Can you give a sample example relative my question? I can not find any example on my schoolbook.
Thanks you!

Last edited: Apr 24, 2007
6. Apr 24, 2007

KTC

AiRAVATA and HallsofIvy already told you. Expand and it cancels out simply. Have you actually tried it?

7. Apr 28, 2007

jiangxiaoyu

Hi
The reasult is the question is wrong. Someone was sure the question was wrong at frist glance. The question can not be allowd by dimension role.

(b + c)×(a × b) may change to (b + c)×(a + b)

In that case, the question was very easy.
Thanks!

8. Apr 29, 2007

Moo Of Doom

Surely you mean sinθ, not cosθ. Just wanted to alert you of this mistake... also, that equation only measures the length, since the cross product yields a vector.