Use Lagrange multipliers to show that the shortest distance from the point (x0,y0,z0) to the plane...

Use Lagrange multipliers to show that the shortest distance from the point (x0,y0,z0)

to the plane ax+by+cz=d

Is it the perpendicular distance?

(Remind yourself of the equation of the line perpendicular to the plane.)

How to solve it

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Use Lagrange multipliers to find the distance from the point (2, 0, −1) to the plane...

Use Lagrange multipliers to find the distance from the point (2, 0, −1) to the plane 4x − 3y + 8z + 1 = 0.

Use Lagrange multipliers to find the point on the given plane that is closest to the...

Use Lagrange multipliers to find the point on the given plane that is closest to the following point. x − y + z = 6; (2, 7, 3)

Use Lagrange multipliers to find the point on the plane 2x + y + 2z =...

Use Lagrange multipliers to find the point on the plane 2x + y + 2z = 6 which is closest to the origin

a.) Find the shortest distance from the point (0,1,2) to any point on the plane x...

a.) Find the shortest distance from the point (0,1,2) to any point on the plane x - 2y +z = 2 by finding the function to optimize, finding its critical points and test for extreme values using the second derivative test. b.) Write the point on the plane whose distance to the point (0,1,2) is the shortest distance found in part a) above. All the work necessary to identify this point would be in part a). You just need to...

Using the methods of Lagrange multipliers, find out the point on the plane 2x+y-2z=5 closest to...

Using the methods of Lagrange multipliers, find out the point on the plane 2x+y-2z=5 closest to the origin. Please show all work.

Starting from the point (x0, y0) = (2,3) of the function f (x) = 4x ^...

Starting from the point (x0, y0) = (2,3) of the function f (x) = 4x ^ 2 - 4xy + 2y ^ 2, it is to choose to proceed according to the Steep Descent Method (x2, y2).

Use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...

Use the method of Lagrange multipliers to find the absolute maximum and minimum values of the function f(x, y, z) = x^2yz^2 subject to the constraint 2x ^2 + 3y^ 2 + 6z^ 2 = 33

2.) Use the method of Lagrange multipliers to find the maximum and minimum values of the...

2.) Use the method of Lagrange multipliers to find the maximum and minimum values of the function ?(?, ?) = ??^2 − 2??^2 given the constraint ?^2 + ?^2 = 2 along with evaluating the critical points of the function, find the absolute extrema of the function ?(?, ?) = ??^2 − 2??^2 in the region ? = {(?, ?)|?^2 + ?^2 ≤ 2}.

use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...

use the method of Lagrange multipliers to find the absolute maximum and minimum values of the function subject to the given constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and y≥0

use Lagrange multipliers to find the maximum and minimum values of f subject to the given...

use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x, y, z) = xyz, x2 + y2 + 4z2 = 12

Subjects