In triangle $AOB$, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$.

Question

In triangle $AOB$, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$. $C$ lies on $AB$ such that $AC:AB = 1:3$. Express $\overrightarrow{OC}$ in terms of $\mathbf{a}$ and $\mathbf{b}$, giving your answer in the simplest form.

Accepted Answer

$\dfrac{2\mathbf a+\mathbf b}{3}$

Vectors - Ratio Theorem and Section Formula

Vectors - Ratio Theorem and Section Formula

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