Step 1 The distance from (2, 0, -3) to a point (x, y, z) is given by d = \\ (x - 2 9 2 1 2 + ( y - 0 0 9 0 ) 2 + ( 2 + 3 0 3 )2. Step 2 We will minimize d2 = (x - 2)2 + y2 + (z + 3)2. Since z = 3 - x - y, we can simplify this to d2 = (x - 2)2 + y2 + (6-x-y 6-x- y Step 3 For f( x, y) = (x - 2)2 + y2 + ( 6 -x - y)2, we get fx(x, y) = 4x + 2y - 16 4x + 2y - 16 and fy(x, y) = 2x + 4y - 12 2x + 4y - 12 Step 4 Solving 4x + 2y - 16 = 0 and 2x + 4y - 12 = 0 simultaneously gives X = y = Recall that z = 3 - x - y, so for this x and y we have z = - 5