(adsbygoogle = window.adsbygoogle || []).push({}); IMPORTANT!!!! ---- what is the geometric intepretation of the gradient vector?

Assume the situation in which I have a slope, a component of a function dependent on x and y, which is at an angle to the xy plane. The gradient vector would be perpendicular to the tangent plane at the point in which i want to find the gradient vector.

However, if i plot the function in the form of a topo map with contour lines, the gradient vector will be perpendicular to the level curve directly towards the higher values of the function parallel to the xy plane.

Hence, we see a contradiction. What i know may be wrong, but can sb clarify this with me and give me an intuitive explanation on the geographical interpretation of the gradient? I know all the math, but I need to UNDERSTAND!

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# IMPORTANT - what is the geometric intepretation of the gradient vector?

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