Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Vectors

12 min read

Vector notation and arithmetic, magnitude, position vectors, and using vectors in geometry.

A vector has magnitude and direction, written as a column $\begin{pmatrix}x\\y\end{pmatrix}$ or $x\mathbf{i}+y\mathbf{j}$ .

Add/subtract component-wise; scalar multiply scales each component.

Magnitude:

\left|\begin{pmatrix}x\\y\end{pmatrix}\right| = \sqrt{x^2+y^2}

Unit vector: divide a vector by its magnitude.

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