Visualization of the Axiom 3b

1. What is the relation between the vectors [math]u[/math] , [math]v[/math] and [math]z[/math] , and the determinants? [br][br]2. Explain the relation between the areas of the parallelograms on the applet and the determinants. Prove your answer with geometric means and with determinants.[br][br]3. Set both points B and C at (1,0) and D at (0,1). Which geometric figure and axiom are obtained?