Vectors and Forces Topic Review summary

Key learning points

• Express forces as $\\mathbf{i},\\mathbf{j}$ components.
• Resultant = vector sum; magnitude via Pythagoras on components.
• Equilibrium ⇔ resultant force is the zero vector.
• Unit vectors give direction; bearing questions need careful angles.
• Moments rarely needed here — focus on force geometry.

Worked example 1 — Resultant

Forces $(3\\mathbf{i}+4\\mathbf{j})$ and $(1\\mathbf{i}-2\\mathbf{j})$.

Working

Add components.

Worked example 2 — Magnitude

$|3\\mathbf{i}-4\\mathbf{j}|$.

Working

3-4-5.

Worked example 3 — Practice point 1

Express forces as $\\\\mathbf{i},\\\\mathbf{j}$ components.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Practice point 2

Apply this idea from the Topic Review: Resultant = vector sum; magnitude via Pythagoras on components.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.