Problem Set 1Problem 1.1 Force Vector ResultantThe riveted brackets supports two forces. Determine the angle θ so thatthe resultant force is directed along the negative x-axis. What is the magni-tude of the resultant force?Figure P1.1: Problem 1.1Problem 1.2 Force Magnitude MinimizationThe boat is to be pulled onto the shore using two ropes. If the resultantforce is to be 80 lbs. directed along the keel a − a as shown, determine themagnitudes of forces T and P acting in each rope and the angle θ of P sothat the magnitude of P is minimum.Figure P1.2: Problem 1.2Problem 1.3 Force Vector AdditionDetermine the magnitude of the resultant vector FR= F1+ F2and itsdirection, measured counterclockwise from the positive x-axis.Figure P1.3: Problem 1.3Problem 1.4 Addition of Coplanar Force SystemsDetermine the magnitude of the resultant force and its direction, mea-sured clockwise from the positive x-axis.Figure P1.4: Problem 1.4Problem 1.5 Force Resultant in 3-DThe beam is subjected to the two force shown. Express each force inCartesian vector form and determine the magnitude and coordinate directionangles of the resultant force.Figure P1.5: Problem 1.5Problem 1.6 Force Vector Coordinate AnglesDetermine the magnitude and coordinate direction angles of F3so thatthe resultant of the three forces is zero.Figure P1.6: Problem 1.6Problem 1.7 Force Directed Along a LineThe window is held open by the cable AB. Determine the length of thecable and express the 30 N force acting at A along the cable as a Cartesianvector.Figure P1.7: Problem 1.7Problem 1.8 Force Directed Along a Structural MemberDetermine the position (x, y, 0) for fixing cable BA so that the resultantof the forces exerted on the pole is directed along its axis, from B towardsO, and has a magnitude of 1 kN. What is the magnitude of F3?Figure P1.8: Problem 1.8Problem 1.9 The cube in Fig. P1.9 has the sides equal to l = 1.a) Find the direction cosines of the resultant v = v1+ v2+ v3+ v4.b) Determine the angle between the vectors v2and v3.c) Find the projection of the vector v2on the vector v4.d) Calculate v2· v4, v2× v4, v1· (v2× v3), (v2× v3)× v4, and v2× (v3× v4).xyzıjkv1v2v3v4Figure P1.9: Problem 1.9Problem 1.10 Figure P1.10 represents the vectors v1, v2, v3, and v4acting on a cube with the side l = 2. The magnitude of the forces arev1= V = 2 and v2= v3= v4= 2 V .a) Find the resultant and the direction cosines of the resultant v = v1+v2+ v3+ v4.b) Determine the angle between the vectors v1and v3.c) Find the projection of the vector v4on the resultant vector v.d) Calculate v2· v, v1× v2, and v2× v4.Oxyzıjkv1v2v3v4Figure P1.10: Problem