Pre-Calculus Help?

A 5-lb force acting in the direction of (5, -3) moves and object just left over 12 ft. from point (0, 6) to (7, -4). Find the work done to move the object to the nearest foot-pound.
a. 11 ft. * lbs
b. 34 ft. * lbs
c. 56 ft. * lbs
d. 61 ft. * lbs

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  1. work = force * distance
    so, how far between the points?

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  2. direction of force = 5 i - 3 j
    make that a unit vector
    sqrt (25 + 9) = sqrt (34)
    so Force vector F = (5/sqrt34)(5i-3j)

    direction of motion vector = 7 i -10 j
    make that a unit vector
    sqrt(49 + 100) = sqrt(149)
    so motion vector
    D = (12/sqrt149) (7i-10 j)

    Work = F dot D = (5/sqrt34)(12/sqrt149)(35+30)
    =.843(65) = 54.8 foot pounds

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  3. so was the answer choice c. 56 ft?

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  4. The correct answer is C

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