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Vectors
O-Level E Math
Vector Basics
$$\left|\begin{pmatrix} x \\ y \end{pmatrix}\right| = \sqrt{x^2 + y^2}$$
Length (magnitude) of a vector
$$\overrightarrow{AB} = k\,\overrightarrow{CD}$$
Parallel vectors
$$\overrightarrow{AB} = k\,\overrightarrow{AC}$$
Collinear points
Position Vectors
Position vectors $\overrightarrow{OP},\; \overrightarrow{OA},\; \overrightarrow{OB}$ all start from the origin $O$.
$$\overrightarrow{OP} = \begin{pmatrix} 2 \\ -3 \end{pmatrix} \;\Leftrightarrow\; P(2,\,-3)$$
Column vectors ↔ coordinates
Connecting Vectors
$$\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB}$$
From $A$ to $O$, then from $O$ to $B$.
Formulas for the Singapore O-Level Elementary Mathematics syllabus