Suppose that an object hangs from three ropes which point in the directions of the vectors...

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Suppose that an object hangs from three ropes which point in the directions of the vectors (2, 2, 1), (-2, -1, 2), and (4,0,3). (Assume that the positive z-axis points directly upward.) If the tension in the first of the three ropes in the list above is 240 pounds, determine the weight of the object. (Hint: You can either start by assuming that the first vector has magnitude 240, or you can find any set of vectors in the appropriate directions that "balance," and then scale them appropriately. Note that knowing the direction of a tension vector does NOT tell you anything about its magnitude.) Suppose that an object hangs from three ropes which point in the directions of the vectors (2, 2, 1), (-2, -1, 2), and (4,0,3). (Assume that the positive z-axis points directly upward.) If the tension in the first of the three ropes in the list above is 240 pounds, determine the weight of the object. (Hint: You can either start by assuming that the first vector has magnitude 240, or you can find any set of vectors in the appropriate directions that "balance," and then scale them appropriately. Note that knowing the direction of a tension vector does NOT tell you anything about its magnitude.)