Vectors — Collinear points PPT lesson summary

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

Add components.

Worked example 2 — Scalar multiple

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

Working

Multiply each component.

Worked example 3 — Magnitude

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

Working

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

Worked example 4 — Reverse

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

Working

Opposite direction.

Full slides and practice PDFs

This page is a short, searchable overview of the PPT lesson for revision and search engines. Download the PowerPoint for classroom teaching, then use the companion worksheet and answers when available.