Scalar Triple Product in Determinant Form

Scalar Triple Product in Determinant Form

If:

$$\vec a=a_1\hat i+a_2\hat j+a_3\hat k$$

$$\vec b=b_1\hat i+b_2\hat j+b_3\hat k$$

$$\vec c=c_1\hat i+c_2\hat j+c_3\hat k$$

then:

$$\vec a\cdot(\vec b\times\vec c)=\begin{vmatrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{vmatrix}$$

Usage

- Used for quick numerical evaluation of scalar triple products.