It should make sense that momentum is a vector quantity because to have momentum, an object must have a velocity, and velocity includes direction.

For the rocket below, it's momentum would be to the right.

If the rocket has a mass of 2000Kg and is moving at 500m/s, what is its momentum?

p = m*v = 2000Kg*500m/s = 1000000Kg*m/s to the right

Here is a little animation of an inelastic collision.  Note that vectors are used to solve the problem.