ballaholic8
New member
- Joined
- Nov 1, 2008
- Messages
- 5
Cross product Homework help
- Thread starter ballaholic8
- Start date
A cross product is built from determinants.
\(\displaystyle \begin{vmatrix}i&j&k\\u_{1}&u_{2}&u_{3}\\1&2&3\end{vmatrix}=i\begin{vmatrix}u_{2}&u_{3}\\2&3\end{vmatrix}-j\begin{vmatrix}u_{1}&u_{3}\\1&3\end{vmatrix}+k\begin{vmatrix}u_{1}&u_{2}\\1&2\end{vmatrix}\)
Remember, a 2X2 determinant is \(\displaystyle \begin{vmatrix}a_{1}&a_{2}\\b_{1}&b_{2}\end{vmatrix}=a_{1}b_{2}-a_{2}b_{1}\)
You can build a system of equations and solve for \(\displaystyle u_{1}, \;\ u_{2}, \;\ u_{3}\)
\(\displaystyle \begin{vmatrix}i&j&k\\u_{1}&u_{2}&u_{3}\\1&2&3\end{vmatrix}=i\begin{vmatrix}u_{2}&u_{3}\\2&3\end{vmatrix}-j\begin{vmatrix}u_{1}&u_{3}\\1&3\end{vmatrix}+k\begin{vmatrix}u_{1}&u_{2}\\1&2\end{vmatrix}\)
Remember, a 2X2 determinant is \(\displaystyle \begin{vmatrix}a_{1}&a_{2}\\b_{1}&b_{2}\end{vmatrix}=a_{1}b_{2}-a_{2}b_{1}\)
You can build a system of equations and solve for \(\displaystyle u_{1}, \;\ u_{2}, \;\ u_{3}\)
