Question

Find the coordinates of the point (x, y, z) on the plane z = 1 x + 2 y + 4 which is closest to the origin.

I got (-1,-2,1) but it's wrong...

Answer 1

not (0, -2, 0)?

Answer 2

nope that also is not right.... :(

Answer 3

LaGrange's method is needed.

Example:
"Subject: The closest point to origin

Let x + y + 3z = 7 represent a plane. We find the closest point to
the origin in this plane by [d/[n]^2] * n. In this case n = (1,1,3);
d = 7; [n]^2 = 1^2 + 1^2 + 3^2 = 11; then the vector that gives us the
closest point is (7/11, 7/11, 21/11).

http://mathforum.org/library/drmath/view/66802.html