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.??
Best Answer
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.