show that unit vector normal to the surface n= ∇φ ÷ | ∇φ | . find n for the ellipsoid.
φ = a(x^2) + b(y^2) +c(z^2)
Given:
φ=ax2+by2+cz2φ = ax^2 + by^2+cz^2φ=ax2+by2+cz2
The gradient of scalar field is given by
Hence
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