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) = x² + y² +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 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 =
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) = x² + y² +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 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 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image 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 =
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