A scalar quantity can be repesented by a single number. Examples of scalars are temperature, salinity, volume, hydrostatic pressure, distance, time, etc. A vector quantity represents a set of three scalar quantities or numbers which have something in common and are collectively referred to as a vector.
Examples are velocity, force, acceleration, gradient of a scalar, vorticity, etc.
In each case three numbers must be used to completely describe the quantity referred to. The meanings of the numbers depend upon the coordinates selected for describing the particular vector. For example, if we choose to describe a velocity in rectilinear coordinates, we would then be required to specify the componnents of the velocity for each of the three mutually perpendicular coordinates. An illustration for the right hand rectilinear coordinate system x , y , z is shown in Fig. We could also represent this same vector by the values of quantities representing the polar coordinates of the end point of the vector which emanates from the origin.