CAIE IGCSE Mathematics Extended Vector Geometry Proofs

Practise using vector expressions and line ratios to locate points, solve geometric constraints and justify parallel, collinear or trapezium relationships.

Exam points

calculate a point's position vector from a stated ratio along a segment or an extended line
show two lines are parallel by deriving one displacement vector as a scalar multiple of the other
prove three points are collinear by giving a common direction vector and the required shared point

Figure for Question E7.4.4 Use vectors to reason and to solve geometric problems question 1 — CAIE IGCSE Mathematics Extended

$\overrightarrow{O T}=\mathbf{t}, \overrightarrow{O U}=\mathbf{u}$ and U Y=2 Y T.

$\quad Z$ is on OT and YZ is parallel to UO.

Find $\overrightarrow{O Z}$ in terms of t and/or u.
Give your answer in its simplest form.

\overrightarrow{O Z}=

$\overrightarrow{OZ}=\frac{2}{3}\mathbf{t}$
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E7.4.4 Use vectors to reason and to solve geometric problems question 1