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How do I solve this vector geometry question?

  1. Oct 20, 2008 #1
    1. The problem statement, all variables and given/known data

    4. Consider the following two lines:

    L1: [1 2 1] + s [2 -1 1] , L2 = [3 0 1] + t [1 1 2]


    (by the way, all of those are column vectors. I just don't know how to format them correctly.)

    (a) These two lines intersect at a point P . Find the co-ordinates of P .

    (b) What is the cosine of the acute angle θ between these two lines ?



    3. The attempt at a solution

    Well for a), I don't know if we are supposed to get the normal vector or not. If so, then I know to do the cross product. If that's not the proper solution then can I merely do P1P2 = P2 - P1, or is that completely irrelevant? I'm just really confused about the wording!
     
  2. jcsd
  3. Oct 20, 2008 #2
    If they intersect at point P, then the x, y and z coordinates of each line are the same at that point right?
     
  4. Oct 20, 2008 #3
    I don't understand what you mean. Each line has separate points and different direction vectors as well. :S
     
  5. Oct 20, 2008 #4
    They have a lot of separate points, but one special point P they have in common. If this point is given by P = [p1 p2 p3] then you would agree that 1+2s = p1 for some s and 3+t = p1 for some t right? It looks like you've got the makings of a set of linear equations.
     
  6. Oct 21, 2008 #5

    HallsofIvy

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    For example, the x coordinate of L1 is given by 1+2s while the x coordinate is given by 3+ t. Where the lines intersect, those must be the same: 1+ 2s= 3+ t. The same is true for the y and z coordinates.
     
  7. Oct 21, 2008 #6
    But it says to find the coordinates of P, not the related scalar equations...
     
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