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**Vector Gah!!!!**

Vector questions. Need help on these three.

In ∆OAB, OA = a and OB = b. P is a point on AB such that BP:PA 1:2.

Q is a point on the extension of OP such that OQ = 1.5OP

a) Express BP and OP in terms of ‘a’ and ‘b’.

these are the answers but how do they get it?

BP = (1/3)(a - b)

OP = (1/3)(a + 2b)

b) Show that AQ = -0.5a + b

i have no idea how to prove this

c) Given that BQ = kOA, find the value of k.

once again this is the answer but i dont know how to approach this can someone show me how to get this value thanks

k = 0.5