Consider two non-zero vectors a and b placed in a plane.
(i) Define the sum a+b using a graphical procedure in which b is drawn from the head of a.
(ii) Define an alternative graphical procedure in which a and b share the same initial point and state how the resultant vector is obtained in this construction.
(iii) Draw neat, labelled diagrams for both procedures described in parts (i) and (ii) for the same pair of vectors.
(iv) Using your diagrams, explain why the resultant vectors obtained in (i) and (ii) are identical and hence deduce that a+b=b+a.