**Problem : **
Consider two vectors
*u*
and
*v*
in the plane which comprise two sides of a
triangle. What vector corresponds to the third side?

Either

*u* - *v*
or

*v* - *u*
are acceptable answers. (The difference will be
whether the arrow for the third side points towards

*u*
or towards

*v*
).

**Problem : **
Find the sum of the vectors which make up the vertices of a regular pentagon
centered at the origin.

The sum of the vectors, which you can find using the geometric method for
vector addition, should turn out to be zero. An easy way to see this is by
noticing that if you rotate the pentagon by an angle of

2*Π*/5
, you will
recover exactly the same same pentagon, with exactly the same vectors
defining its vertices. Thus, whatever vector you obtain by adding up the
five vectors, it should remain unchanged under such a rotation. Only the
zero-vector (the origin itself) doesn't move when you rotate the plane,
hence this is the only possible candidate for the result of the sum.