Diketahui titik A(2, -1, 3), titik B(6, 2, 3) dan titik P(6, -3, 7), vektor AB mewakili vektor a. Jarak P terhadap vektor a adalah

[tex]\boxed{d=\dfrac{\left\|\overrightarrow{AP}\times\overrightarrow{AB}\right\|}{\left\|\overrightarrow{AB}\right\|}}[/tex]
[tex]\overrightarrow{AB}=\vec{b}-\vec{a}= \begin{pmatrix}4\\3\\0\end{pmatrix};~~\overrightarrow{AP}=\vec{p}-\vec{a}=\begin{pmatrix}4\\-2\\4\end{pmatrix}[/tex]
[tex]\overrightarrow{AP}\times\overrightarrow{AB}=\begin{vmatrix}i&j&k\\4&-2&4\\4&3&0\end{vmatrix}=\begin{pmatrix}-12\\16\\-20\end{pmatrix}[/tex]
Jadi
[tex]d=\dfrac{\sqrt{(-12)^2+(16)^2+(-20)^2}}{\sqrt{3^2+4^2+0^2}}=\dfrac{20\sqrt{2}}{5}=4\sqrt{2}[/tex]