a.) OA = <3, 4> and OB = <4, -6>. Let C have coordinates (x, y). Then OC = <x, y>.

Therefore <3, 4> = <x, y> + <4, -6> = <x + 4, y - 6>.

Therefore 3 = x + 4 and 4 = y - 6 ....

b.) OD = <1, 24>.

Therefore <1, 24> = h <3, 4> + k <4, -6> = <3h + 4k, 4h - 6k>

Therefore:

1 = 3h + 4k .... (1)

24 = 4h - 6k .... (2)

Solve equations (1) and (2) simultaneously.