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Warning: new definition for   norm
Warning: new definition for   trace

#<h4>Problem</h4>
Show that if the diagonals of a rectangle intersect at right angles
then, the rectangle is a square.
<hr>

> a := vector([a1,a2]); b := s*vector([-a2,a1]);

                                a := [ a1, a2 ]

                              b := s [ - a2, a1 ]

# Here the vectors "a" and "b" denote the sides of a general 
rectangle on the plane. The scalar "s" is the ratio of the 
lengths of the two sides. Here is the picture,
<br>
<center><img src="diagonals.gif" alt="picture here"></center>
<br>

> diag1 := a+b:  diag2 := a-b:

> solve( angle(diag1,diag2) = Pi/2, s);

                                     1, -1

# so yes! it is a square.

>