I was looking into a lecture note online, and we have this function $T(r, θ, φ) = (r \sinθ \cosφ, r \sinθ \sin φ, r \cos θ)$. After calculations, I know that the columns of the derivate of this function are orthogonal to one another. What is a geometric interpretation of this fact?
Derivative of a function has orthogonal columns
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calculus
real-analysis