Question

Area of parallelogram with four vertices using cross product

Answer 1

Answer:

Cross product. The vector $\color{red}{\vc{c}}$ (in red) is the cross product of the vectors $\color{blue}{\vc{a}}$ (in blue) and $\color{green}{\vc{b}}$ (in green), $\color{red}{\vc{c}} = \color{blue}{\vc{a}} \times \color{green}{\vc{b}}$. The parallelogram formed by $\color{blue}{\vc{a}}$ and $\color{green}{\vc{b}}$ is pink on the side where the cross product $\color{red}{\vc{c}}$ points and purple on the opposite side. Using the mouse, you can drag the arrow tips of the vectors $\color{blue}{\vc{a}}$ and $\color{green}{\vc{b}}$ to change these vectors. See how the cross product $\color{red}{\vc{c}}$ and the parallelogram change in response. (You cannot change the red cross product vector $\color{red}{\vc{c}}$ directl