A-Level Maths Edexcel (9MA0)

Understand and use position vectors; calculate the distance between two points represented by position vectors.

$\overrightarrow{OB} - \overrightarrow{OA} = \overrightarrow{AB} = \bold{b} - \bold{a}$

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by

$d^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2$

In three dimensions, the distance $d$ between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by

$d^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2$