- #1
kekido
- 20
- 0
Homework Statement
The height of a hill is given as the following:
[tex]
h \left( x,y \right) =40\, (\left( 4+{x}^{2}+3\,{y}^{2} \right) ^{-1})
[/tex]
There's a stream passes the point (1,1,5) which is on the surface of h. The stream follows the steepest descent. Find the equation of the stream.
Homework Equations
I take this is relevant to the tangent hyperplane of a surface.
Tangent plane at point a is: f(a)+gradient(f(a)) dot (x-a)
The Attempt at a Solution
I think the path of the stream is the intersection of the surface h and a plane orthogonal to the tangent plane at point (1,1,5), but I'm not sure.