Using the Lagrange multipliers method, find the distance of the plane 2x + 2y + 4z = 10 to the point P= (0,0,0). a) Consider the function to minimize as f(x,y,z) = x + y? +z², which is the distance...

Extracted text: Using the Lagrange multipliers method, find the distance of the plane 2x + 2y + 4z = 10 to the point P= (0,0,0). a) Consider the function to minimize as f(x,y,z) = x + y? +z², which is the distance squared from a point (x,y,z) on the plane to the origin (0,0,0). Set up the system of equations which you must solve (the coefficients you must enter can be any number, including zero or one) 2x %3D y+ z = 21 y+ Z = 2x + 2y + 4z = 10 b) Find the value of the Lagrange multiplier 2: c) Find the value of the distance of the plane to the origin distance =