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Homework Help: Really easy vector addition.

  1. Jan 5, 2010 #1
    1. The problem statement, all variables and given/known data

    I have three vectors and I need to find the resultant of the three vectors and direction.

    2. Relevant equations

    *All angles are with the horizontal

    Vector 1 = 18 at an angle of 40 degrees (First Quadrant)
    Vector 2 = 10 at an angle of 72 degrees (Second Quandrant)
    Vector 3 = 22 at an angle of 55 degrees (Third Quadrant)

    3. The attempt at a solution

    In the X I got: 18cos(40) - 10cos(72) - 22cos(55) = -1.9
    In the Y I got: 18sin(40) + 10 sin(72) - 22sin(55) = 3.1

    √(-1.92 + 3.12) = 3.64 is the resultant

    tan-1(3.1/-1.9) = -58.5 degrees is the direction/angle

    I just need confirmation whether this is right or wrong. =)
     
  2. jcsd
  3. Jan 5, 2010 #2

    vela

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    Looks good. Well, almost perfect. You should be a little careful with your terminology.

    The resultant is a vector, the sum of the three vectors, and it has a magnitude and direction. The 3.64 you found is the magnitude of the resultant, not the resultant itself.

    For the direction, you need to be a little careful because arctangent only returns angles between -90 degrees and +90 degrees. You should give a little more information to indicate exactly what the angle is, e.g. which quadrant, measured relative to what, etc.
     
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