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

Question

In parallelogram $OABC$, $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OC}=\mathbf{b}$. The diagonals intersect at $M$. Express $\overrightarrow{OB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$. Express $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$. Explain why the diagonals of a parallelogram bisect each other.

Accepted Answer

(a) $\mathbf{a}+\mathbf{b}$; (b) $\frac12(\mathbf{a}+\mathbf{b})$.

Sec 3/4 E Math T16-Q25 - Vector proof in a parallelogram

Sec 3/4 E Math T16-Q25 - Vector proof in a parallelogram

Solution:

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