(a) Suppose ABCDEF is the vertices of a regular hexagon. Let AB = a and BC = b.
(i) Express the vectors AB ,AC,AD,AE,AF in terms of a and b.
(ii) Find the resultant of the forces represented by the vectors in (i), in terms of AD.
(b) If O is any point within triangle ABC andP , Q and R are midpoints of the sides AB,BC, and CA respectively. Prove that OA + OB + OC = OP + OQ + OR

Question

(a) Suppose ABCDEF is the vertices of a regular hexagon. Let AB =  a and BC =  b. 
(i) Express the vectors AB ,AC,AD,AE,AF in terms of  a and b.
(ii) Find the resultant of the forces represented by the vectors in (i), in terms of AD.
(b) If O is any point  within  triangle ABC andP , Q and R are midpoints of the sides AB,BC, and CA respectively. Prove that OA +  OB + OC =   OP + OQ + OR