Assume perfect sphere lands on a surface given by the function(adsbygoogle = window.adsbygoogle || []).push({});

z = 2x^{2}-3y^{2}at point (2,1,5). I am trying to find a unit vector of the direction in which this perfect sphere will roll.

If I get grad F I'll get a vector field that is perpendicular to the level curves f(x,y) = z = 2x^{2}-3y^{2}. This is going to be the steepest ascent. Thus negative grad F should give the steepest descent.

However, this is still a normal to the level surface. How do I find the direction in which it will roll along the surface?

PS. this is not a homework question. I was studying some differential geometry over the holidays and this problem was given in the book.

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# Grad F of a level curve?

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