Unit vector normal to scalar field

AI Thread Summary
To find a unit vector normal to the surface of the scalar field φ(x,y,z)=x²y+3xyz+5yz², the gradient operator (∇) should be applied to the scalar field. This operation yields a vector that is normal to the surface. To convert this normal vector into a unit vector, it must be divided by its magnitude. The discussion confirms that this method effectively provides the required unit vector normal. The process is straightforward and essential for understanding surface normals in vector calculus.
Reshma
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How do you find a unit vector normal to the surface of scalar field

\phi(x,y,z)=x^2y+3xyz+5yz^2?

Should you apply the \nabla operator to it?
 
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Reshma said:
How do you find a unit vector normal to the surface of scalar field

\phi(x,y,z)=x^2y+3xyz+5yz^2?

Should you apply the \nabla operator to it?

That operation will give you a vector normal to the surface. To find the unit vector, you of course need to divide by its magnitude.

Zz.
 
Thanks..I got the answer!
 
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