Given that position vectors of points A and B are a = vector of point a and b = vectors of point b and C is a point on AB such that AC : CB = 1 : 2. Find the coordinates of the point C.

Question

Given that position vectors of points A and B are a =  and b =  and C is a point on AB such that AC : CB = 1 : 2. Find the coordinates of the point C.

Answer 1

OC = OA + AC

OC = OA + ¹/₃AB
  = a + ¹/₃( a + b)
 =²/₃a + ¹/₃b

∴ C(−⁴/₃, 3)