In parallelogram $OABC$, $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OC}=\mathbf{b}$

Question

In parallelogram $OABC$, $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OC}=\mathbf{b}$. Points $P$ and $Q$ are the midpoints of $AB$ and $BC$ respectively. Express $\overrightarrow{OP}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[2] Express $\overrightarrow{PQ}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[2]

Accepted Answer

(a) $\mathbf{a}+\dfrac12\mathbf{b}$ (b) $\dfrac12(\mathbf{b}-\mathbf{a})$

Midpoints on a parallelogram

Midpoints on a parallelogram

Solution:

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