# Math Insight

### Applet: Scalar triple product

The value of the scalar triple product $(\color{blue}{\vc{a}} \times \color{green}{\vc{b}}) \cdot \color{magenta}{\vc{c}}$ is shown at the top, where the vectors $\color{blue}{\vc{a}}$ (in blue), $\color{green}{\vc{b}}$ (in green), and $\color{magenta}{\vc{c}}$ (in magenta) can changed by dragging their tips with the mouse. The volume of the spanned parallelepiped (outlined) is the magnitude $\|(\color{blue}{\vc{a}} \times \color{green}{\vc{b}}) \cdot \color{magenta}{\vc{c}}\|$. The cross product $\color{blue}{\vc{a}} \times \color{green}{\vc{b}}$ is shown by the red vector; its magnitude is the area of the highlighted parallelogram, which is one face of the parallelepiped.

The three-dimensional perspective of this graph is hard to perceive when the graph is still. If you keep the figure rotating by dragging it with the mouse, you'll see it much better. (Apologies to color blind people for reliance on colors.)