Texts: Notation and conventions: In R^2 (2-dimensional Euclidean space), the vectors i and j denote the standard basis vectors ⟨1, 0⟩ and ⟨0, 1⟩ respectively. In R^3 (3-dimensional Euclidean space), i, j, and k denote the standard basis vectors ⟨1, 0, 0⟩, ⟨0, 1, 0⟩, and ⟨0, 0, 1⟩. Given a vector v in R^2 or R^3, we denote its length by ||v||. All coordinate systems are assumed to be right-handed. Total points: 100. Each numbered question: 10 pts.
4.) Given the vector-valued functions r(t) = ti + 3j + (t^2)k and u(t) = 4i + 3j + k, compute the derivative d/dt (r(t) × u(t)).