The two vectors labelled c are defined to be equal although we
need a shift to move
them exactly on top of each other. Vectors that can be shifted about
are called free vectors.
There is one important situation in which we can't shift the vectors
around. Displacement from a given fixed point such as the origin
is a vector quantity, but the vector is tied
to the fixed point.
The vector r in the drawing above is called the
position vector of the point P from the
fixed origin O, and describes the displacement of P from O. It
must run from O to P and can't be shifted around.