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Dot Product Issues

  1. Jun 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Vector A and four other vectors that have the same magnitude but differ in orientation. a) Which of those other four vectors have the same dot product with A? b) Which have a negative dot product with A?
    http://img195.imageshack.us/img195/7079/40191924.th.jpg [Broken]
    (Those circle things between the arrows are supposed to be thetas. I suck at drawing quickies in paint.)

    2. Relevant equations
    a*b = abcos(theta)


    3. The attempt at a solution
    For a) I recognized that they would all have the same dot product with a, since the magnitude of all the vectors are the same, as is their angle. What I don't get is the answer to b. It says D and E. Shouldn't the dot products all be positive? In the equation a and b are positive (and always will be), and cos(theta) is positive in this case, how would the dot product turn out to be negative?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 22, 2009 #2
    What is the angle between D and A?
     
  4. Jun 22, 2009 #3
    180 - theta. :blushing:
     
  5. Jun 22, 2009 #4
    By the image, it looks like [itex]\theta[/itex] is acute, so 180 - [itex]\theta[/itex] must be obtuse. From this, you should be able to guess the sign of the cosine of the angle.
     
  6. Jun 22, 2009 #5
    Yeah, I understand where I went wrong. Thanks.
     
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