We use vectors to generalize our description of motion to
more than one spatial dimension.
It is very straight forward to do this. The position vector,
, of the particle in conjunction
with a chosen origin determines its time dependent position. As for
the one dimensional case knowing you have in hand
the full information there is to be had about the motion of the particle.
We often resolve into its time dependent components
along N mutually orthogonal directions. N is the number of dimensions
we are trying to keep track of. For motion in a plane we need just
keep track of N=2 dimensions.
That is our equation for really contain two
functions specifying position
versus time along two orthogonal directions.