From: The dynamics of particles and of rigid, elastic, and fluid bodies. Being lectures on mathematical physics (1912) Webster, Arthur Gordon, 1863-1923
In mathematics we have to consider two sorts of quantities,
The distance between two points x1, y1, z1,
x2, y2, z2
s = √ ( (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2 )
is a scalar, whereas the geometrical difference in position of the two points is known only when we specify not merely the length, but also the direction of the line joining them.