A vector quantity has both magnitude and a specific direction. To describe a vector fully you must give its size, its unit and its direction. A force of 10 N is an incomplete description. A force of 10 N to the right is complete.
Displacement, velocity, acceleration, force, weight and momentum are vector quantities. A velocity of 5 m/s north and a weight of 600 N downwards are both full descriptions. A vector can be shown as an arrow: the length of the arrow shows the magnitude and the way it points shows the direction.
To show opposite directions, choose one direction as positive. If right is positive, a velocity of 4 m/s to the left has a negative sign. The sign shows the direction.
