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