Scalar Triple Product Calculator

The scalar triple product is a mathematical operation involving three vectors in 3D space, producing a scalar quantity. It is calculated as:

\[ \text{Scalar Triple Product} = \mathbf{A} \cdot (\mathbf{B} \times \mathbf{C}) \]

Example Calculation

Given vectors:

\[ \mathbf{A} = (1, 2, 3), \quad \mathbf{B} = (4, 5, 6), \quad \mathbf{C} = (7, 8, 9) \]

The cross product \(\mathbf{B} \times \mathbf{C}\) is:

\[ \begin{bmatrix}
5 \times 9 - 6 \times 8 \
6 \times 7 - 4 \times 9 \
4 \times 8 - 5 \times 7
\end{bmatrix} = (-3, 6, -3) \]

The scalar triple product is:

\[ 1 \times (-3) + 2 \times 6 + 3 \times (-3) = 0 \]

This calculation is useful in vector calculus, geometry, and determining volumes of parallelepipeds formed by the three vectors.