Read up your textbook or lecture notes on Lagrange multipliers. It is not as difficult as it sounds.
However, you need to master you algebra and basic calculus, which I believe should not be a problem.
To put it in the least words possible, we attempt to optimize (maximize or minimize) a function f(x,y,z) subject to the constraint g(x,y,z).
The suggested objective function is the square of the distance from the origin, which therefore is
The constraint is
We now introduce a Lagrange multiplier, λ, to form a new function Λ:
Now apply partial differentiation with respect to each of the variables, and equate result to zero:
Add the original constraint equation:
Now solve the system of 4 equations in x,y,z and λ and voilą!
x=1, y=-2, z=3, L=2.
So the distance is
How can we tell if this is correct?
This is not too difficult... in this particular case.
The shortest distance from a point (origin 0,0,0) to a plane is the perpendicular distance, given by the well-known formula:
and the square of the minimum distance
which checks with our Lagrange multiplier answer.
Answer this Question
Linear Algebra - In 3-space, a plane abc is spanned by three points a, b, c. The...
Math - How do you: Find the shortest distance, to two decimal places from the ...
calculus - Use Lagrange multipliers to find the max/min values of the function f...
7th grade math Ms. Sue please - 2. Shelly sews a blanket that has an area of 170...
Geometry - Martin wants to use coordinate geometry to prove that the opposite ...
????Math Question????8th grade adv.math - Algebra! How is the distance formula ...
maths - geometry - In a space with an orthonormal coordinate system consider the...
physics - A toy plane p starts flying from point A along a straight horizontal ...
geometry - A point is moving in a plane in such a way that its distance from the...
trigonometry - The angle of elevation of the top of a tower to point A on the ...