# Homework Help: Determinates to Calculate Cross Product

1. Sep 18, 2011

### QuarkCharmer

1. The problem statement, all variables and given/known data
Not really a homework problem, just a general question.

2. Relevant equations
Sorry, I don't yet know how to create arrays/matrices in latex (this is a gif)

3. The attempt at a solution
In the above image, why is $c_{1}$ positive, $c_{2}$ negative, and $c_{3}$ positive?

Aside from that, I think I understand the rest. I would assume c from the formula to be the unit vectors denoting direction, A would be the first vector in the product, and B would be the second. From there,

$c_{1}$ times $(a_{2}b_{3} - b_{2}a_{3})$

would be the $c_{1}$ component of the product and so on...

But why would the y/j component be negative in the formula?

2. Sep 18, 2011

### LCKurtz

3. Sep 18, 2011

### QuarkCharmer

Ahh, I see. So it's going to alternate every time as the exponent (i+j) becomes odd/even. I can see how this would get really tedious for matrices larger than 3x3.

Thanks for the information!

4. Sep 18, 2011

### flyingpig

It's just the nature of it isn't it? It's like looking at the mirror