Vectors anyone?

OABC is a parallelogram


P is the point on AC such that AP = 2/3 AC.








OA= 6a. OC = 6c


Find the vector OP.


Give you answer in terms of a and c.

Vectors anyone?
Assuming a and c are vectors and not constants, you can find OP by





OP = OA + 2/3*AC





AC = OC - OA





so OP = OA + 2/3*(OC - OA)





or


OP = 1/3*OA + 2/3*OC = 1/3*(6a + 2*6c)





OP = 2a + 4c
Reply:Jonsmart's work is valid until the last line. He really needs to write it as a vector, that is compute the two unit vectors in directions of the vectors OA and OC . The answer is then (1/18a) OA + (2/18c)OC .