Quick questions on Geometric proofs with vectors: parallel, perpendicular, midpoint and ratio properties

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is vertex order in the parallelogram condition?

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It is

\overrightarrow{AB} = \overrightarrow{DC}

(so the figure closes as

ABCD

), not

\overrightarrow{AB} = \overrightarrow{CD}

. Getting the order wrong reverses a side.

What is section-formula labels swapped?

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For ratio

m : n

from

A

, the position vector is

\frac{n\mathbf{a} + m\mathbf{b}}{m + n}

: the weights cross over. The midpoint is the special case

1 : 1

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