3.7.1—Standard notations for vectors

A vector has size and direction; in 2D or 3D write components as a column or i,j,k combination. The magnitude of (a,b,c) is √(a²+b²+c²).

Keep vectors distinct from points, which describe position relative to an origin. A unit vector has magnitude 1 and preserves direction.

The vector (3,4) has magnitude 5; its unit vector is (3/5,4/5).

The coordinates of a point and the components of a displacement are not interchangeable unless the origin and direction are specified.