Learning pack · IGCSE handout

Vectors in a triangle

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). IGCSE Additional Mathematics (CIE 0606) PPT lesson on vectors in a triangle and finding an intersection point P. Use this page to revise the vector geometry set-up, then download the step-by-step study slides.

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

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (1)📖 Full summary

Files: ·

Full topic summary

IGCSE Additional Mathematics (CIE 0606) PPT lesson on vectors in a triangle and finding an intersection point P. Use this page to revise the vector geometry set-up, then download the step-by-step study slides.

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

\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.

🎬 Topic videos

Vectors in a Triangle — Find Intersection P | CIE IGCSE Additional Maths (0606)
IMProjectLessons · 4 min
Vectors in a triangle: X on AB, Y on OA, P = OX ∩ BY; express OP two ways; solve λ, μ by equating coefficients (section/ratio style). Matches slides 3f4a3ae9 (Vectors in a Triangle — Find Intersection P). Primary CIE 0606; also 0607 vectors, 9709, and IB AA/AI vector geometry.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Vectors in a triangle PPT lesson summary.