Position & Displacement Vectors (DP IB Analysis & Approaches (AA): HL): Revision Note

A position vector describes the position of a point in relation to the origin

The position vector of point A is written with the notation $\mathit{a}=\overrightarrow{\mathrm{OA}}$ 

• The origin is always denoted O

The individual components of a position vector are the coordinates of the point

• For example, the point with coordinates (3, -2, -1) has position vector $3\mathit{i}–2\mathit{j}–\mathit{k}$

A displacement vector describes the shortest route between any two points

The displacement vector of point B from the point A is written with the notation $\overrightarrow{\mathrm{AB}}$

A position vector is a displacement vector of a point from the origin

A displacement vector between two points can be written in terms of the displacement vectors using a third point

• For example, $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{CB}}$

A displacement vector can be written in terms of its position vectors

•  For example, $\overrightarrow{\mathrm{AB}}$ can be written in terms of $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OB}}$

  • $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{AO}}+\overrightarrow{\mathrm{OB}\mathrm{ }}$

  • This can be rewritten as $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{OB}}-\overrightarrow{\mathrm{OA}\mathrm{ }}$