Question

does anyone know how to compute the unit normal vector to surface S : x^2+y^2+z^2 = 1? Thanks

Answer 1

I do believe you need to have a point on the surface to compute that. You will also need to define out of that surface a level curve that the point is on and change it to a space curve eq with its vector components. Or I guess you could take the partial derivatives at that point, and make two vector equations for tangent lines, then take the cross product of the two line equations, and it will give you the normal vector, then divide that by the magnitude of that normal vector, to make it a unit normal vector. I like dealing with the normal vectors via space curves, but either way will work. The unit normal from a space curve is the second deriv of the space curve/ the magnitude of it at a point. Good luck.

Answer 2

No, there is no point on the surface. Actually this is a part of another problem. The original question is:Suppose a temperature function is given in R3 by the formula T(x,y,z) = x^2 + y^2 + z^2. let s be the unit sphere x^2 + y^2 + z^2 = 1 oriented with the outward normal. Find the heat flux across the surface S if k = 1.

Answer 3

you have to choose one, otherwise you can't compute it

Answer 4

the gradient is a vector normal to the surface

Answer 5

the normal and the gradient are the same vector; but the gradient at times requires a point to establish itself; when you obtain the normal; just divide itself by its magnitude to get to a unit length

Answer 6

gradient can be calculated at some point

Answer 7

:)

Answer 8

You get that thing, the gradient or the dell or what they call it by partial fractions and that gives you a vector, unitize that vector