accompanied when its rate of change vector has non-zero perpendicular component to the original vector. This can be shown to be the case by considering a vector which is parameterized by some variable for which:

Which also gives a relation of rate of change of unit vector by taking , to be such a vector: showing that vector is perpendicular to the vector, .

From:

since the first term is parallel to and the second perpendicular to it, we can conclude in general that the parallel and perpendicular components

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