Answer to Question #155353 in Classical Mechanics for Xoxo

Question

1. Prove that the area of a parallelogram with sides A and B is |A×B|. 

Answer 1

By defenition$|A×B|=ABsin\alpha,$

Area of parallelogram equals two areas of triangles $\frac 12 AB sin \alpha,$ i.e. $ABsin\alpha,$ where $\alpha$ is angle befween A and B.