Chapter 12.4, Problem 46E

(a) Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the plane is

$d=\frac{\left|a\cdot \left(b\times c\right)\right|}{\left|a\times b\right|}$

where $a\text{ = }\stackrel{\to }{QR}$, $b\text{ = }\stackrel{\to }{QS}$, and $c\text{ = }\stackrel{\to }{QP}$.

(b) Use the formula in part (a) to find the distance from the point $P\left(2,1,4\right)$ to the plane through the points $Q\left(1,0,0\right)$, $R\left(0,2,0\right)$, and $S\left(0,0,3\right)$.