Vectors

About this lab: Vectors

Interactive simulation for Cambridge IGCSE Mathematics 0580 vectors: drag column vectors on a grid, add them tip to tail and with a parallelogram, subtract by adding the negative, multiply by a scalar to get parallel vectors, find the magnitude with Pythagoras, use position vectors to find a midpoint or a point dividing a line in a ratio, and step through vector proofs that lines are parallel and points are collinear.

IGCSE Mathematics 0580, topics 7.2 to 7.4 (Extended). Column vectors, adding, subtracting and multiplying vectors, magnitude, position vectors, and vector proofs of parallel lines and collinear points.

Vectors is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 7 Transformations and vectors, sections 7.2 Vectors in two dimensions (Extended), 7.3 Magnitude of a vector (Extended), 7.4 Vector geometry (Extended)). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 6 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

• 7.2 Vectors in two dimensions (Extended). Lessons: Vectors in two dimensions.
• 7.3 Magnitude of a vector (Extended). Lessons: Magnitude of a vector.
• 7.4 Vector geometry (Extended). Lessons: Vector geometry.

Full syllabus map: IGCSE Mathematics 0580 topic 7.

How to use this simulation

1. 1. Column vectors.
2. 2. Add and subtract.
3. 3. Scalar multiples.
4. 4. Magnitude.
5. 5. Position vectors.
6. 6. Vector proofs.
7. The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

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