Consider the vector function r(t) that has unit tangent vector 1 T(t) VI+$₁² (1,1,21), 0 ≤ t ≤ 2. √1+5t2 Suppose that the tangent vector of r(t) has magnitude ✓1+5t². Find the curvature x of the curve r(t) at a general point t. (a) (b) (c) (d) Find the vector function r(t) such that r(0) = 0. Compute the principal unit normal vector N of r(t). Hence, determine the vector dT/ds.

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