# Math Help - Equality of products.

1. ## Equality of products.

I'm sorry if this has been asked, I've searched around and couldn't find it.

$a + b + c = 0$

where a, b and c are vectors.

Q) Show that a*b = b*c = c*a

Thanks.

2. Are you using an asterix to represent dot product, cross product, componentwise multiplication, or something else entirely?

3. If you mean dot product, this isn't true, Take a to be a unit vector, b= -a, c= 0. Then $a\cdot b= |a|^2= 1$ while $a\cdot c= b\cdot c= 0$.

If you mean the cross product, it still isn't true. Take $a= \vec{i}$, $b=-\vec{i}+ \vec{j}$ and $c= -\vec{j}$. Then $a\times b= b\times c= \vec{k}$, but $a\times c= -\vec{k}$.

So what does "*" mean?

4. It could be the cross product. The last product is c times a, not the other way around.

Edit: And if it is the cross product, you may find it useful to write c = -a-b.

You then need to check that b*c and c*a are both equal to a*b (recall that the cross product is linear in both variables (like any good product), and that x*x=0 for all x).

5. i was referring to the cross product, sorry if I wasn't clear enough :L

6. Have you solved the problem yet?

7. How many dimensions are the vectors?

8. @Prove It, It doesn't state how many dimensions but I'm assuming 3? Not entirely sue