# Calculating the vector product

1. Feb 9, 2009

### intenzxboi

i have a question i'm trying to find the cross product of the vector but don't know which formula to use.

the first one is
i(....) + j(....) + k (....)
and the other one is the same as this one but has a negative sign
i(....) - j(....) + k (....)

what is the difference and which formula should i use?

2. Feb 9, 2009

### Tom Mattson

Staff Emeritus
There is only one formula. You compute the following (formal) determinant.

$$\hat{A}\times\hat{B} = \left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k}\\a_1 & a_2 & a_3\\b_1 & b_2 & b_3\end{array}\right|$$

where $\hat{A}=\left<a_1,a_2,a_3\right>$ and $\hat{B}=\left<b_1,b_2,b_3\right>$.