The diagram shows triangle $$\(O A B\)$$ Diagram NOT accurately drawn $$\(M\)$$ is the point on $$\(O B\)$$ such that $$\(O M: M B=1: 2\)$$ $$\(N\)$$ is the midpoint of $$\(A B\)$$ $$\(P\)$$ is the point of intersection of $$\(O N\)$$ and $$\(A M\)$$ Using a vector method, find $$\(\overrightarrow{O P}\)$$ as a simplified expression in terms of $$\(\mathbf{a}\)$$ and $$\(\mathbf{b}\)$$ Show your working clearly. $$\[ \overrightarrow{O P}= \]$$

Answer:

Knowledge points:

Solution: