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Math Help - vector question

  1. #1
    Senior Member euclid2's Avatar
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    vector question

    given two vectors, \vec{u} and \vec{v} such that \vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| explain what you know about these two vectors.
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    A Plied Mathematician
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    What ideas have you had so far?
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  3. #3
    Senior Member euclid2's Avatar
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    the only thing i can think of is that one of them has a length of 0.
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  4. #4
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    Yes, if either of the vectors, or both, are the zero vector, the equation will hold. What if neither are nonzero? Can you still satisfy the equation?
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  5. #5
    MHF Contributor Unknown008's Avatar
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    How do you find the angle between two vectors usually?

    Maybe this will hint you at the answer
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  6. #6
    Senior Member euclid2's Avatar
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    does this mean there is no angle between the two vectors? (0 deg)
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  7. #7
    A Plied Mathematician
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    Right. That's the only situation where the angle between the two vectors has a cosine of one.
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  8. #8
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    And, of course, having an angle of "0" between them means the vector point in the same direction- one is a multiple of the other. (We should also point out that cos(180)= 0. Two angles that point in opposite directions have dot product 0. Of course, one is still a multiple of the other, just with negative multiplier.)
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  9. #9
    A Plied Mathematician
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    Reply to HallsofIvy:

    I think you meant to say that \cos(180^{\circ})=-1. If two vectors are pointed in the opposite direction, then the cosine of their angle is negative one. Two vectors that are orthogonal have a zero dot product.
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