Chapter 1, Problem 20P

The distance d from a point P (x_p,y_p,z_p) to the line that passes through the two points A (x_A,y_A,z_A) and B (x_B,y_B,z_B) can be calculated by d=2S/r where r is the distance between the points A and B, given by $r=\sqrt{{(x_B-x_A)}^2+{(y_B-y_A)}^2+{(z_B-z_A)}^2}$ and S is the area of the triangle defined by the three points calculated by where $s=\sqrt{s_1^2+s_2^2+s_3^3}$where

$\begin{array}{l}{s}_1=x_P{y}_A+x_A{y}_B+x_B{y}_P-(y_P{x}_A+y_A{x}_B+y_B{x}_P)\\ s_2=y_P{z}_A+y_A{z}_B+y_B{z}_P-(z_P{y}_A+z_A{y}_B+z_B{y}_P)\\ s_3=x_P{z}_A+x_A{z}_B+x_B{z}_P-(z_P{x}_A+z_A{x}_B+z_B{x}_P)\end{array}$. Determine the distance of point P(2,6,-1) from the line that passes through point A(-2, -1.5,-3) and point B(-2.5,6,4). First define the variables x_P,y_P,z_P, x_A, y_A, z_A, x_B,y_B, and z_B,and then use the variable tocalculate s₁, s₂, s₃. and r. Finally calculate S and d.