Question

Hi
can any one tell me
Why gradient vector is orthogonal to tangent ?
with an example

Answer 1

F(x,y) = x - y(x)

Fx = 1
Fy = -1y'

grad(F) = <1,-1y'>

notice that F(x,y) = x-y(x) is equalvalent to: y = x, with a tangent of y'=1 at any x

Answer 2

the gradient vector is a normal vector, and a normal vector is always perp to a tangent vector

Answer 3

. that's a sphere and it is the easiest way to see how they perp together