i cannot find the value of 'lambda'
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OC = OA + AC = a + 2b
BC = BO + OC = (-b) + (a + 2b) = a + b
OQ = OB + BQ = OB + (1/3)BC = b + (1/3)(a + b) = (1/3)a + (4/3)b
i) OR = OP + PR = (1/2)OA + hPQ
Now, PQ = PO + OQ = -(1/2)OA + OQ = -(1/2)a + (1/3)a + (4/3)b = -(1/6)a + (4/3)b
OR = (1/2)OA + hPQ = (1/2)a + h[-(1/6)a + (4/3)b]
(I'll let you simplify that.)
OR = k OC
(1/2)a + h[-(1/6)a + (4/3)b] = k[a + 2b]
From here equate the coefficients of a on each side of the equation and the coefficients of b on each side of the equation. Two equations in two unknowns, h and k, so you can solve this.
I have to go. See if you can carry on from here.