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Position vector with ratio?

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Use vectors to find the position vector of point P if P divides AB in the ratio 3:2 given A (-1,6,4) and B (4,1,-1)

    3. The attempt at a solution

    Well I assume it's sort of like finding the midpoint, except I would do something like (-1+4)/1.5 etc.

    Am I correct? Do I just divide the sum of the numbers by 3/2 hence the ratio? or am I going about this the wrong way?
  2. jcsd
  3. Feb 4, 2009 #2


    Staff: Mentor

    Point P is 3/5 the way along from A to B. When you divide something in the ratio 3:2, one part will be 3/5 of the total and the other will be 2/5 of the total.

    It shouldn't be too hard to find that point.
    Assuming for the moment that the coordinates of P are (x, y, z), the position vector of point P will be the vector (x - (-1), y - 6, z - 4). This vector has the same direction as AP and the same magnitude.
  4. Feb 7, 2009 #3
    Is this a descent answer?

    If AP:PB=3:2 then AP:AB=3:(3+2)=3:5
    P = A + (B-A)*3/5
    P = (-1,6,4)+(5,-5,-5)*3/5
    P = (-1,6,4)+(3,-3,-3)
    P = (2,3,1)

    Am I correct? Can anybody clarify?
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