OABC is a square. M is the midpoint of OA, and Q divides BC in the ratio

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OABC is a square. M is the midpoint of OA, and Q divides BC in the ratio 1 : 3. AC and MQ meet at P.


a. If OA(vector) = a and OC(vector) = c, express OP(vector) in terms of a and c.


b. Show that P divides AC in the ratio 2 : 3.


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