Vectors are defined as quantities that behave as displacements (distances with specified directions) do relative to coordinate systems and when added together, etc. In other words all true vectors have the same properties as do displacements. We know that if we walk a path due east for 1 km and then walk due north for 1 km that we end up being 1.41 km from our starting point ("as the crow flies") and we are now northeast of our starting point at an angle of 450 north of east. If force is a vector, then it must have these same properties. A force of 1 N to the east added to a force of 1 N to the north should add together to give a net force of 1.41 N directed to the northeast at an angle of 450. We want to demonstrate this property of forces