Dot product and angle between two vectors

Exercises

Set the sliders so that

and

. 1) Move the heads of the vectors

and

around the circumferences. What is the behaviour of

? Which are the maximum and minimum values? How are these values related to the angle between these vectors? 2) Which vectors satisfy

? Next, change the moduli of

and

to a value of your choice. Repeat 1) and 2). Relate your answers to the following result: if

denotes the angle between

and

, then