Multiplication by Scalars and Components
A vector can be multiplied by a number or a scalar. ca is in the same direction of a, and the magnitude |ca|=c|a|.
A vector of unit magnitude is called a unit vector. For any vector a, a/|a| is a unit vector along a, often written as
To describe a vector quantitatively, we use a right-handed coordinate system with x, y, and z axes, and the unit vectors along the three axes are i, j, k, respectively.
Suppose a point has coordinates (x,y,z), then the vector r=xi+yj+zk represents a position vector pointing from the origin to the point. The numbers (x,y,z) are called the components of r.