Set the sliders so that [math]\left|u\right|=2[/math] and [math]\left|v\right|=1[/math].[br]1) Move the heads of the vectors [math]u[/math] and [math]v[/math] around the circumferences. What is the behaviour of [math]u\cdot v[/math]? Which are the maximum and minimum values? How are these values related to the angle between these vectors?[br]2) Which vectors satisfy [math]u\cdot v=0[/math] ?[br][br]Next, change the moduli of [math]u[/math] and [math]v[/math] to a value of your choice. Repeat 1) and 2).[br][br]Relate your answers to the following result: if [math]\alpha[/math] denotes the angle between [math]u[/math] and [math]v[/math], then[br][center][math]cos\alpha=\frac{u\cdot v}{\left|u\right|\left|v\right|}[/math][/center][br]