Chapter 12.1, Problem 102E

(a)

To determine

To show: The point $P\left(\frac{ad}{D^2},\frac{bd}{D^2},\frac{cd}{D^2}\right)$ is nearest to the origin and it is in the plane $ax+by+cz=d$ if the least distance from the plane to the origin is $\frac{\left|d\right|}{D}$.

(b)

To determine

To show: The least distance from the point $P_0\left(x_0,y_0,z_0\right)$ to the plane $ax+by+cz=d$ is $\frac{\left|a{x}_0+b{y}_0+c{z}_0-d\right|}{D}$.