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ankit sharma Grade: 12
        

For a tangent plane to a surface, why is the normal vector for this plane equal to the gradient vector? Or is it not?

6 years ago

Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
										

DEAR ANKIT,


You have to be a bit more precise: if a surface is defined by

LaTeX Code: f(\\mathbf{x})=0

then

LaTeX Code: \\nabla f\\big|_{\\mathbf{x}_0}

is a vector tangent to the surface at point x0. This is because it is orthogonal to the velocities of all possible curves that pass through x0:

LaTeX Code: 0=df=\\nabla f\\cdot\\mathbf{v}


 




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Sagar Singh


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6 years ago
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