Ta có:
\(\overrightarrow {AB} = \overrightarrow {OB} - \overrightarrow {OA} \)
Mà:
\(\eqalign{
& \overrightarrow {OB} = {x_B}\overrightarrow i + {y_B}\overrightarrow j \cr
& \overrightarrow {OA} = {x_A}\overrightarrow i + {y_A}\overrightarrow j \cr
& \overrightarrow {AB} = ({x_B}\overrightarrow i + {y_B}\overrightarrow j ) - ({x_A}\overrightarrow i + {y_A}\overrightarrow j ) \cr
& \,\,\,\,\,\,\,\,\, = \,({x_B} - {x_A})\overrightarrow i \, + ({y_B} - {y_A})\overrightarrow j \cr} \)
Vậy: \(\overrightarrow {AB} = ({x_B} - {x_A};\,{y_B} - {y_A})\)
