Problem 4 Vector-valued functions. Let H(t) = (cost, e-*, 0), G(t) = (t,0, Int), and F(t) = (t3, 1, -t) . Consider the scalar triple product h(t) = H(t) . (G(t) x F(t)) (i) Compute dt h(t) using the Cross and the Dot Product Rules for differentiating. (ii) Compute h(t), differentiate it, and compare with the result in (i)Problem 5 Integration of Vector-Valued Functions. Consider the vector-valued function defined by r(t) = (v2t, 3t2, 0). Find the definite integrals. () r(t) dt I|r(t)1| at