Texts: Given a vector function r(t) = t i + (3t + 1)j + (t^2 − 5) k, where t ∈ ℝ.
(a) Find the magnitude of the tangent vector at t = 0. The quantity is given by √c, where c > 0. Write the value of c. [10]
(b) Find the curvature of r at t = 0. If the curvature of r(0) is 1/k, where k > 0, find the value of k.