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To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. F1=-60 i +150 j +45 k lb. F2=120 lband forms the following angles with the x, y, and zaxes, respectively: a=52.7°, ß=68.1°, and ?=134.6°. F3=90 lb, forms the angle ?=30° with the z axis, and forms the angle ?=27° between the x axis and the projection of F3 in the xy plane. Part A - Resultant of adding F1 and F3 Find the resultant of adding F1 and F3. Express your answer in component form. R13=? Part B - Resultant of adding F1 and F2 and F3 Find the resultant of adding F1, F2, and F3. Express your answer in component form. R123=? Part C - Direction of a resultant For the given forces, F1, F2, and F3, find the three direction angles aR, ßR, and ?R between the resultant force R123 found in Part B and the x, y, and z axes, respectively. aR, ßR, ?R=? Part D - Find the direction angle a when given direction angles ß and ? As shown, a force of 280 lb acts at the tip of a tower. Two of the force's direction angles are known, ßR1=39° and ?R1=63°, that define the angles between the force and the y and z axes, respectively. Find aR1, the angle between the x axis and the force.
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