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Math Help - Angle between vectors

  1. #1
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    Angle between vectors

    I can do the full equation but the problem is trying to find the angle between two vectors,

    So if I had the problem

    Find angle between these two given vectors:
    A = (2,1,-3)
    B = (1,-1,1)

    A.B = -2

    |a| = sqrt14
    |b| = sqrt3

    so

    -2/sqrt42 = -0.309

    I know cos(thetre) = A . B / a b

    but I'm still not sure how to go about finding the angle
    how do I work out the angle?? Iam quite new to vectors so Iam guessing this is quite obvious,
    Please can someone point it out for me!!
    I have the answer 108 degrees in my notes I just dont know how to get that!!
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  2. #2
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    Use the arccosine function.
    \Theta  = \arccos \left( {\frac{{A \cdot B}}{{\left\| A \right\|\left\| B \right\|}}} \right).
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  3. #3
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    Thanks, is that the only way to solve this type of question? Its no big deal I just I cant see arccos written in my notes
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  4. #4
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    turns out this is the way I'm supposed to do it ..
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  5. #5
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    Quote Originally Posted by dankelly View Post
    Thanks, is that the only way to solve this type of question? Its no big deal I just I cant see arccos written in my notes
    I find that really odd if true.
    The arccosine function is one of the most useful in the study of vectors.
    Its domain is \left[ { - 1,1} \right] and its range is \left[ {0,\pi } \right] \approx \left[ {0,180^ \circ  } \right].

    Even a minimal scientific calculator will have a preprogrammed button for the arccosine. It may be signed as \cos ^{ - 1} .
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