Distance from a point to a plane in space
Given the point $P=(1, 2, 3)$, find the distance between $P$ and the plane $\pi$:
$$\pi: 4x+2y-4z+3=0$$
$$\text{d}(P,\pi)=\dfrac{|A\cdot p_1+B\cdot p_2+C\cdot p_3+D|} {\sqrt{A^2+B^2+C^2}} = \dfrac{|4\cdot1+2\cdot2-4\cdot3+3|}{\sqrt{4^2+2^2+(-4)^2}} = \dfrac{1}{6}$$
$$\text{d}(P,\pi)= \dfrac{1}{6}$$