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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Rajat Jain posted an Question
May 20, 2020 • 11:39 am
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Vit.e., grad t is normal to the surtace f(x, y, z) = c. vect theorem lf n be a unit vector normal to the level surface f(x, y, z) = c at a point p in th directi
EXPLAIN THE STATEMENT OF THIS THEOREM. VIT.e., grad t iS normal to the surtace f(X, y, Z) = C. vect Theorem lf n be a unit vector normal to the level surface f(x, y, z) = c at a point P in th direction of f increasing andn be the distance of P from a fixed point A in the direction of n, then. df grad f= dn Proof Rv thac
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Anuj s. Best Answer
The gradient of a function is normal to the level sets because it is defined that way. The gradient of a function is not the natural derivative. When you have a function, f, defined on some Euclidean space (more generally, a Riemannian manifold) then its derivative at a point, say x, is a function dxf on tangent vectors. feel free to ask any doubt we will discuss