Calculus and Vectors

13. Find the torque produced by a cyclist exerting a force of F = [45, 90, 130]N on the shaft- pedal d = [12, 17, 14]cm long. a) (-950, 930, -315) b) 3890 c) 19874 d) 1866625 14. Given a = [3, -1, 4]& c = [-2, 6, t], find t so that a and c are perpendicular. a) 4 b) -3 c) -4 d) 3 15. Given u = [-12, 6, k]& v = [4, -2, 4], find k so that u and u are parallel. a) 4 b) -3 c) 6 d) -12 16. An object moves along a straight line in such a way that its position is s(t) = -5t3 + 17t2, in which t represents the time in seconds. What is the object's acceleration at 2.7 seconds? a) -47 b) -17.55 c) 17 d) -81 17. Find the unit vector of a = [-3, -7, 4]. a) [-3,-7,4] VIA [-3, -7, 4] C) (V14' V14' V74' V74 18. Derive y = -2(3-7x) a) -2In3(3-7x) b) -14ln7(3-7x) c) 7In2(3-7x) d) 14In3(3-7x)1 23. Using first principles, determine the derivative of f (x) = V4x+7 24. Determine the corresponding Cartesian equation. L1: T = [4, -3, 5] + t[2, 0, 3], t E R and L2: T = [4, -3, 5] + s[5, 1, -1], s ER