Lagrange Multiplier functions Gradients direction

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when the contour of one function is tangible to the contour of another function. I know contour and gradient are orthogonal to each other. Shouldn't be the gradient(del g- pink) of the g(x,y) be opposite side(i.e., 180) to the gradient(del f - light blue) of f(x,y)??

Kindly do correct me if I am wrong.

Gradient directions of Lagrange Multipliers