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Math Help - Finding the angle between to vectors

  1. #1
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    Finding the angle between to vectors

    im trying to Find the angle between to vectors, when they are placed tail to tail
    how do you do this...(in 2D and 3D)...im trying to use the law of cosines, manipped so cos(theta) is on one side......but im not getting the right answer

    please explain the process, and the answer to this

    [cos19, sin19] and [cos54, sin54]
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stones44 View Post
    im trying to Find the angle between to vectors, when they are placed tail to tail
    how do you do this...(in 2D and 3D)...im trying to use the law of cosines, manipped so cos(theta) is on one side......but im not getting the right answer

    please explain the process, and the answer to this

    [cos19, sin19] and [cos54, sin54]
    use the dot product:

    u \cdot v = |u||v| \cos \theta

    where u and v are vectors and \theta is the angle between them, this works in 2D and 3D
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  3. #3
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    ok thanks

    now to find |u| or |v| in 3D

    so..

    [a,b,c]

    root(a^2 + b^2) =x

    root(x^2 + c^2) =|u|

    right?
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  4. #4
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    u = \left\langle {a,b,c} \right\rangle \quad  \Rightarrow \quad \left\| u \right\| = \sqrt {a^2  + b^2  + c^2 }

    If u & v are vectors, the angle between them is
    \phi  = \arccos \left( {\frac{{u \cdot v}}{{\left\| u \right\|\left\| v \right\|}}} \right)<br />
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