Learning pack · IGCSE handout

Vectors — Collinear points

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). IGCSE Additional Mathematics (CIE 0606) PPT lesson on proving points are collinear with vectors. This summary outlines the method, notation, and a typical exam-style chain of reasoning before you open the slide deck.

Resources at the top · full summary · videos with short notes below.

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Full topic summary

IGCSE Additional Mathematics (CIE 0606) PPT lesson on proving points are collinear with vectors. This summary outlines the method, notation, and a typical exam-style chain of reasoning before you open the slide deck.

Key learning points

Write each point as a position vector from a shared origin.
Points A, B, C are collinear when $\overrightarrow{AB}=k\overrightarrow{AC}$ for a scalar $k$ .
Keep vector letters consistent ( $\mathbf{a}$ , $\mathbf{b}$ ) and state the scalar clearly.
End with a sentence: therefore the points lie on a straight line.

Worked example 1 — Addition

$\mathbf{a}=\begin{pmatrix}2\\1\end{pmatrix}$ , $\mathbf{b}=\begin{pmatrix}3\\-4\end{pmatrix}$ . $\mathbf{a}+\mathbf{b}$ ?

Working

\begin{pmatrix}5\\-3\end{pmatrix}

Add components.

Worked example 2 — Scalar multiple

$3\begin{pmatrix}2\\-1\end{pmatrix}$ .

Working

\begin{pmatrix}6\\-3\end{pmatrix}

Multiply each component.

Worked example 3 — Magnitude

Find $\left|\begin{pmatrix}3\\4\end{pmatrix}\right|$ .

Working

5

$\sqrt{3^2+4^2}$ .

Worked example 4 — Reverse

If $\overrightarrow{AB}=\mathbf{v}$ , then $\overrightarrow{BA}$ ?

Working

-\mathbf{v}

Opposite direction.

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