Math Transition To College Math - Unit 11: Vectors
1) What is a vector?

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2) What do vectors represent?

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3) In the study of vectors, what kind of quantity can be described by magnitude only? Give two examples.

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4) A vector placed on a rectangular coordinate plane is said to be in standard position when the initial point is located where?

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For the next five problems, find the corresponding standard vector XY with endpoints as indicated.

5) X(9, –4), Y(7, 5)

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6) X(–6, –3), Y(9, 1)

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7) X(–2, 3), Y(5, 4)

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8) X(3.2, –2.1), Y(–7.4, –2.6)

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9) X(–21, 7), Y(36, –14)

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10) What is the magnitude of a vector?

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11) Find the magnitude for the vector.

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12) Find the magnitude for the vector.

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13) Find the magnitude for the vector.

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14) Find the magnitude for the vector.

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15) Find the magnitude for the vector.

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16) Perform the indicated operation.

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17) Perform the indicated operations.

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18) Perform the indicated operation.

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19) Perform the indicated operations.

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20) Perform the indicated operations.

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21) List four algebraic properties that hold true for vector addition.

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22) List three algebraic properties that hold true for scalar multiplication.

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23) Name two methods that may be used to add vectors.

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For the next five problems, use either method given above to solve the problems.

24) Two forces of 25 pounds and 45 pounds act on a point in the plane. If the angle between the directions of the two forces is 120 degrees, find the magnitude of the resultant force. Use the "Law of Cosines" to solve the problem.

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25) Two forces of 37 pounds and 13 pounds act on a point in the plane. If the angle between the directions of the two forces is 78 degrees, find the magnitude of the resultant force. Use the "Law of Cosines" to solve the problem.

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26) A 13 pound force and a 12 pound force produce a 20 pound resultant force. Find the angle between the directions of the 13 pound force and the resultant force in the figure. Round the answer to the nearest whole number.

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27) The angle between the directions of two forces is 113 degrees. One of the forces has magnitude 219 pounds, and the resultant force has magnitude 242 pounds. Find the angle between the 219 pound force and the resultant force. Use the diagram below and the “Law of Sines” to solve the problem. Round the answer to the nearest tenth.

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28) Two forces act on a point in the plane, producing a resultant force with magnitude 487 pounds. The magnitude of one force is 232 pounds. Find the magnitude of the other force if the angle between the 232 pound force and the resultant force is 27.5 degrees. Use the “Law of Cosines” to solve the problem. Round the answer to the nearest whole number.

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