Changes

Examine this equation, and make sure you understand how each of the matrices on the right hand side were formed.  Once we have reached this point, we can use our definition of a 2x2 determinant to arrive at a value.

Examine this equation, and make sure you understand how each of the matrices on the right hand side were formed.  Once we have reached this point, we can use our definition of a 2x2 determinant to arrive at a value.

We now arrive at a means of calculating the cross product of two vectors.  It turns out that the definition we gave of cross product amounts to

We now arrive at a means of calculating the cross product of two vectors.  It [[Calc3.2/Cross Product Proof|turns out]] that the definition we gave of cross product amounts to

<math>\vec{u}\times\vec{w}=\begin{vmatrix}\vec{i}&\vec{j}&\vec{k}\\u_1&u_2&u_3\\w_1&w_2&w_3\end{vmatrix} \ </math>

<math>\vec{u}\times\vec{w}=\begin{vmatrix}\vec{i}&\vec{j}&\vec{k}\\u_1&u_2&u_3\\w_1&w_2&w_3\end{vmatrix} \ </math>