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Math Help - vectors

  1. #1
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    vectors

    Find the resultant of the following vectors:
    a) 50 units due east and b) 100 units 30 degrees north of west.

    the resultant can be found by using the law of cosines. however, i don't understand why you change the addition sign to the subtraction sign to get the correct answer:

    by not changing the formula you get:
    R^2 = a^2 + b^2 - 2ab*cos(angle)
    R^2 = 100^2 + 50^2 - 2(100)(50)(cos150) = 145 units

    by changing the sign you get:
    R^2 = a^2 + b^2 + 2ab*cos(angle)
    R^2 = 100^2 + 50^2 + 2(100)(50)(cos150) = 62 units

    62 units is the correct answer, but i do not understand why the sign must be changed?
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  2. #2
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    the angle should be 30 degrees ...

     R = \sqrt{100^2 + 50^2 - 2(100)(50)\cos(30)}<br />
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