1

I am confused about whether gradients are parallel to surfaces or perpendicular to the surfaces of the given equation.

A gradient of a function is given as a vector whose components in x,y,z direction are partial derivatives in x,y and z of the given function.

Partial derivatives (compared with derivatives in 1D) are parallel to the surface and give the rate of change (https://www.youtube.com/watch?v=GkB4vW16QHI).

While in this lecture(https://youtu.be/2XraaWefBd8?t=1359) the gradient gives the vector perpendicular to the surface.

Am is missing something.??

daniel
  • 79
  • You need to be careful about which function you’re talking about taking the gradient of. See, for example, the discussion in the answer to this question. – amd Apr 11 '20 at 21:08

1 Answers1

2

Turns out its perpendicular as well as parallel. Gradient of a level curve/surface is perpendicular to the level curve/surface but Gradient of a function is always tangent to the surface of the funtion. Now any surface can be made a level surface by transferring all the constants to one side of the function and then assuming it as a new function which is constant, hence a level curve/surface.

daniel
  • 79