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Math Help - why to calculate unit vectors before calculating their dot product?

  1. #1
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    Unhappy why to calculate unit vectors before calculating their dot product?

    why to calculate unit vectors before calculating their dot product?

    Could someone explain this to me?
    Last edited by mr fantastic; March 3rd 2011 at 03:20 AM. Reason: Copied title to main body of post.
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  2. #2
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    Quote Originally Posted by problady View Post
    Could someone explain this to me?
    What?

    I don't understand what you are trying to do.

    Can you post the exact question you are working on?
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    Lets assume I have many vectors with different lengths and I would like to calculate their angle etc. To do that I need dot product ... but since they have different length is suggested to normalize them (unit vector them) and later take the dot product... so my question is why we need to "unit vector them" first etc. THANKS
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  4. #4
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    Quote Originally Posted by problady View Post
    Lets assume I have many vectors with different lengths and I would like to calculate their angle etc. To do that I need dot product ... but since they have different length is suggested to normalize them (unit vector them) and later take the dot product... so my question is why we need to "unit vector them" first etc. THANKS
    Still makes no sense. Post a specific and concrete question.
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    Quote Originally Posted by problady View Post
    Lets assume I have many vectors with different lengths and I would like to calculate their angle etc. To do that I need dot product ... but since they have different length is suggested to normalize them (unit vector them) and later take the dot product... so my question is why we need to "unit vector them" first etc. THANKS
    I would say you don't. It's six of one, a half-dozen of the other. The formula for dot product is

    \mathbf{a}\cdot\mathbf{b}=\|\mathbf{a}\|\,\|\mathb  f{b}\|\cos(\theta), or

    \cos(\theta)=\dfrac{\mathbf{a}\cdot\mathbf{b}}{\|\  mathbf{a}\|\,\|\mathbf{b}\|},

    where \theta is the angle between them. If \mathbf{a},\mathbf{b} are unit vectors (you've normalized them), then the formula reduces down to

    \mathbf{a}\cdot\mathbf{b}=\cos(\theta).

    However, you've had to do the work of normalizing. So it's either normalize first and use a slightly simplified dot product formula, or just use the full dot product formula. You'll have to divide by the lengths either way.
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