بردار در فضا

اگر $M\left(p,q,r\right)$ یک نقطه مفروض باشد، آن‌گاه:

$\begin{array}{l}\left|MA\right|=\sqrt{{\left(x_A-x_M\right)}^2+{\left(y_A-y_M\right)}^2+{\left(z_A-z_M\right)}^2}=\sqrt{{\left(p-p\right)}^2+{\left(0-q\right)}^2+{\left(0-r\right)}^2}\\ \left|MA\right|=\sqrt{q^2+r^2}\end{array}$

$\begin{array}{l}\left|MB\right|=\sqrt{{\left(x_A-x_M\right)}^2+{\left(y_A-y_M\right)}^2+{\left(z_A-z_M\right)}^2}=\sqrt{{\left(0-p\right)}^2+{\left(q-q\right)}^2+{\left(0-r\right)}^2}\\ \\ \left|MB\right|=\sqrt{p^2+r^2}\end{array}$

$\begin{array}{l}\left|MC\right|=\sqrt{{\left(x_A-x_M\right)}^2+{\left(y_A-y_M\right)}^2+{\left(z_A-z_M\right)}^2}=\sqrt{{\left(0-p\right)}^2+{\left(0-q\right)}^2+{\left(r-r\right)}^2}\\ \\ \left|MC\right|=\sqrt{p^2+q^2}\end{array}$