So I understand most of the properties of cross products. However I ran into a small complication.
I get that $i\times j = k$, $j\times k = i$. I also understand that $k \times j = -i$ and that $k\times k = j\times j = i\times i = 0$.
But what happens when you have $-k\times k$? Does that also equal $0$, or something else?
There is another algebraic property of the cross product such that $(ra) \times b = r(a \times b)$ where $a, b$ are vectors and $r$ is a constant. (http://en.wikipedia.org/wiki/Cross_product)
Since you said that $k \times k = 0$, we can write $(-k) \times k = -(k \times k) = -0 = 0$