Dot Product Issues

  • Thread starter Pupil
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  • #1
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Homework Statement


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.)

Homework Equations


a*b = abcos(theta)


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?
 
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Answers and Replies

  • #2
1,013
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What is the angle between D and A?
 
  • #4
1,013
70
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.
 
  • #5
124
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Yeah, I understand where I went wrong. Thanks.
 

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