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Multivariable & Vectorhard
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Given a smooth surface defined implicitly by F(x,y,z)=x2+2y2+3z2−6=0F(x, y, z) = x^2 + 2y^2 + 3z^2 - 6 = 0F(x,y,z)=x2+2y2+3z2−6=0, find the gradient ∇F\nabla F∇F at the point (1,1,1)(1, 1, 1)(1,1,1), and determine which vector is normal to the surface at this point.