Example 2.3.1: Displacement vector

The field point has $r=3a_x-a_y+4a_z$ and the source point $r{}^{\prime }=-3a_x+a_y+a_z$. By Eq. (2.3.3),

Its magnitude, the distance between the two points, is $R=\sqrt{36+4+9}=\sqrt{49}=7$. Check of direction: starting from $\mathrm{Q}(-3,1,1)$ and adding $R$ we arrive at $(-3+6,1-2,1+3)=(3,-1,4)$, which is $\mathrm{P}$.