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Math Help - Easy Ratio Vector Question, but not sure if answer is wrong

  1. #1
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    Easy Ratio Vector Question, but not sure if answer is wrong

    Let A, B be points in R3 with position vectors

    a (7,-2,3)
    b (1,-5,0)

    Let Q be the point on AB such that AQ= 2/3 AB
    Find q, the position vector of Q

    2. Relevant equations
    The back of the book says the answer is: (2,-3,-1)

    3. The attempt at a solution
    First, I found the vector of AB: (-6,-3,-3)
    So Q should be: a+(2/3)(AB)
    ie: (7,-2,3)+(-4,-2,-2)
    =(3,-4,1)
    Which is different to the answer given by the book.
    Did i do anything wrong?
    Thanks
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  2. #2
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    Re: Easy Ratio Vector Question, but not sure if answer is wrong

    Quote Originally Posted by geoff18 View Post
    Let A, B be points in R3 with position vectors

    a (7,-2,3)
    b (1,-5,0)

    Let Q be the point on AB such that AQ= 2/3 AB
    Find q, the position vector of Q

    2. Relevant equations
    The back of the book says the answer is: (2,-3,-1) <-- that's definitely wrong

    3. The attempt at a solution
    First, I found the vector of AB: (-6,-3,-3)
    So Q should be: a+(2/3)(AB)
    ie: (7,-2,3)+(-4,-2,-2)
    =(3,-4,1)
    Which is different to the answer given by the book.
    Did i do anything wrong?
    Thanks
    The vectors \overrightarrow{AQ} and \overrightarrow{AB} are not collinear.
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