Which Formula Should I Use for Calculating the Vector Product?

[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?

 

[quantumdude]

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>.