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.

OC = OA + ACOC = OA + ^{1}/_{3}AB = a + ^{1}/_{3}( a + b) =^{2}/_{3}a + ^{1}/_{3}b∴ C(−^{4}/_{3}, 3)

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