Find the point on the plane z = 8x + 10y + 1 closest to the point P=(1, 0, 0).

Answer 1

8x + 10y - z + 1 = 0
shortest distance from (1,0,0) to this plane
= |8(1) + 10(0) - 1(0) + 1|/√(8^2 + 10^2 + 1^2)
= 9/√165 or 3√165/55