Unit 13.2 Worked Example 3

(i)

Find the exact shortest distance of the point \(A\left( 3,1,-2 \right)\) to the plane \({{p}_{1}}:x-3y+2z=-5\).

(ii)

Find the coordinates of foot of perpendicular of point \(B\left( 7,4,-5 \right)\) to plane \({{p}_{1}}:x-3y+2z=-5\).