Vectors in a triangle PPT lesson summary

Key learning points

• Label position vectors of triangle vertices from a fixed origin.
• Express points dividing sides in a given ratio with section formula.
• Find intersection P by equating two parametric forms of lines inside the triangle.
• Compare coefficients of independent vectors to solve for the parameters.

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.