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Find length of segment AB

  1. Apr 18, 2010 #1
    1. The problem statement:

    The line r=(-8,-6,-1) + s(2,2,1) intersects the xz- and yz-coordinates planes at points A and B, respectively. Determine the length of line segment AB.


    2. Relevant equations



    3. The attempt at a solution

    I know that for the line, x= -8 + 2s, y= -6 + 2s, and z= -1 + s. I think the normals to the xz- and yz- planes are (0,1,0) and (1,0,0) respectively. Do I just stick the parametric equations of the line into the Cartesian equation of each of the planes to get something or do I have to use different numbers?
     
  2. jcsd
  3. Apr 18, 2010 #2

    Mark44

    Staff: Mentor



    Knowing the normals to the two coordinate planes isn't useful in this problem, but something that is useful is that every point on the x-z plane has a y coordinate of 0. There is a similar property for every point on the y-z plane. Can you use this information in your problem?
     
  4. Apr 18, 2010 #3
    How?
     
  5. Apr 18, 2010 #4

    Mark44

    Staff: Mentor

    You know that the line intersections points A and B, and that these points are on, respectively, the x-z and y-z coordinate planes. What do you know about point A? Point B?
     
  6. Apr 19, 2010 #5
    That A has a y-value of 0 and B has an x-value of 0. Now what?
     
  7. Apr 19, 2010 #6

    Mark44

    Staff: Mentor

    Use your equation of the line. The two points have to be on the line, right? x= -8 + 2s, y= -6 + 2s, and z= -1 + s.
     
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