Question

3. Lagrange multipliers Consider a plane described by the equation nx - k, and consider a point a not on the plane (here, bold symbols (n, x, and a) are vectors, plain symbols (k) are scalars). a) Using the method of Lagrange multipliers, find the point 3 (in the plane) that is closest to the point a. Note: n is a unit vector (i.e., nTn = 1). Hint: Your objective function J(x), which you want to minimize, is distance. Your constraint is that the point you choose must lie in the plane (it can't just be any point). b) Solve the unconstrained problem for comparison (the point does not need to lie in the plane, just minimize the distance)

Answer 1

Sol Consides the distane eueen -lhe vecho and χ . the distance Shauld be inimum g the Plane

2(x-ブ 2- Bur lies on the plane . .

K-na