Giả sử \(M\left( {x;y;z} \right)\) thỏa mãn \(\overrightarrow {MA} = k\overrightarrow {MB} \) với \(k \ne 1\).
Ta có \(\overrightarrow {MA} = \left( {{x_1} - x;{y_1} - y;{z_1} - z} \right),\overrightarrow {MB} = \left( {{x_2} - x;{y_2} - y;{z_2} - z} \right)\)\(\overrightarrow {MA} = k\overrightarrow {MB} \Leftrightarrow \left\{ \matrix{
{x_1} - x = k\left( {{x_2} - x} \right) \hfill \cr
{y_1} - y = k\left( {{y_2} - y} \right) \hfill \cr
{z_1} - z = k\left( {{z_2} - z} \right) \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x = {{{x_1} - k{x_2}} \over {1 - k}} \hfill \cr
y = {{{y_1} - k{y_2}} \over {1 - k}} \hfill \cr
z = {{{z_1} - k{z_2}} \over {1 - k}} \hfill \cr} \right.\)
