The Geometric Construction of Vectors

A vector is represented mathematically by a directed line segment, the length of which corresponds to the magnitude of the vector, whilst 

The arrow indicating direction is placed at any appropriate point on the line segment. We have chosen for the most part to place the arrow at the mid poirrt 

Vectors are represented by symbols such as a, b. and their respective magnitudes are given by a, A, . or just a, b. An alternative notation, OP, is sometimes used when we wish to describe a displacement in space between two points (in this case, points O and P). 

The vectors a and b are said to be equal if their magnitudes and directions are the same, irrespective of the locations of their respective initial points. Hence, any directed line segment with the same length and direction as a is represented by a. 

A unit vector is a vector having unit magnitude (or length). Unit vectors are symbolized by a, A. and correspond to the vectors a, b. divided by their own magnitude. For example  

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