Find the unit normal vector z=xy to the surface at the point
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if you want to find unit normal vector to a surface, you need to find the gradient of the surface.
The surface is z -xy = 0
grad (z - xy) = -y i -x j + k
(i, j, k are directional unit vectors for X, Y and Z axis in Cartesian Coordinate system)
This vector is normal to the surface.
To make it with value of unity,
(-yi -xj + k)/sqrt((-y)^2 + (-x)^2 +1)
The surface is z -xy = 0
grad (z - xy) = -y i -x j + k
(i, j, k are directional unit vectors for X, Y and Z axis in Cartesian Coordinate system)
This vector is normal to the surface.
To make it with value of unity,
(-yi -xj + k)/sqrt((-y)^2 + (-x)^2 +1)
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