A rod of negligible mass is attached to a vertical beam by a hinge at point A and a horizontal cable at point B, as shown in the figure. The angle between the rod and the beam is and the distance between points A and B is L. (a) Enter an expression for the vector r extending from A to B in terms of L and and the unit vectors i and j. Use the coordinate system shown in the figure. (b) Let the tension in the cable be T = Ti. Enter a vector expression for the torque ₁ on the rod about the hinge due to that tension, in terms of T, L, , and the unit vectors i, j, k. (c) Given the values T = 484.9 N, L = 1.21 m, and = 33.7, calculate the magnitude of the torque ₁, in newton-meters. (d) A force F = -Fj acts on the rod at point C, whose distance from the hinge is fL, 0 < f < 1. Refer to the figure. Enter a vector expression for the torque ₂ on the rod about the hinge due to the force F, in terms of F, L, f, , and the unit vectors i, j, k. (e) For the values L = 1.21 m, = 33.7, T = 484.9 N, and f = 0.842, calculate the magnitude F of the force F, in newtons, needed to balance the torque from the tension in the cable.