Using appropriately labelled diagrams to support your answer, explain in detail how the position vector r(t) of a point P(x, y, z) in R³, on a space curve C, yields the following important results, r' (t) Ir' (t) and explain in your own words how the notion of the derivative is involved, i.e, r(t+h) - r(t) (a) The unit tangent vector T(t) = r' (t)= lim h-0 (b) Using a clear diagram explain how we use the unit tangent vector T(t) to find the normal and binormal vectors, N(t) and B(t), respectively. (c) If r(t)= c, a constant, prove that r' (t) is orthogonal to r(t), and also that, r' (t) x r(t) = 0.

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