how to calculate magnitude of vector and position vector?

Consider a point P in space.It can be specified by three coordinates x,y,z. Another way to specify this point is by joining this point P from origin O.Then the vector  specifies the position in space and is called the position vectior as it specifies a point(position) in space.

Let ,  can be resolved into three components along x,y and z axes.Let ,  and  be the unit vector along x, y and z axes.

then position vector can be written as 

The magnitude of a vector can be determined by using Pythagorean theorem.The magnitude of position vector  is

 

It represents the distance from the origin to that point on the coordinate system