Find the point on the plane $x+2y+3z = 1$, which is nearest to the point $(-1,0,1)$ by Lagrange’s multiplier method.

Question

Find the point on the plane $x+2y+3z = 1$, which is nearest to the point $(-1,0,1)$ by Lagrange’s multiplier method.

Answer 1

Hint

$${\min (x+1)^2+y^2+(z-1)^2\\\text{s. t.}\\x+2y+3z-1=0}$$