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