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The answer is P = P(5/4, -5/4, -1/2)

Can someone explain to me the concept of this? I don't quite understand it. So basically we are suppose to find a vector P that is 1/4 away from (P1 - P2)? The solution manual does (1/4)P1 + (3/4)P2 = P. Why?

Thanks in advance.