How do I draw vector addition on a cartesian coordinate system?

Say if I have 2 vectors, a and b:


a = (3,4)


b = (5,1)





I know that vector a + vector b = (8,5).





But how do I draw it and how can I prove or show that the resultant indeed is (8,5). The thing that confuses me is the location of the vector tails. Should the tails be in the origin for a and b?





Please help!|||Starting at the origin, draw vector a.





Then, starting at the head of a, draw vector b.





Then, draw a vector from the origin to the head of b.





This vector is a+b|||use the head to tail method. place one vectors head at the end of the others tail and draw the resultant. and then use the formula c=sqrt(a^2+b^2) and to find the direction you take tan(B/A)