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Line intersecting plane

  1. Jun 29, 2004 #1
    How would I find the points of intersection of the line x= 3+2t , y= 7+8t , z=-2+t , that is, l(t) = (3+2t,7+8t,-2+t) with the coordinate plane?

    Also, how would I prove using vectors that the line segment joining the mdpoints of two sides of a triangle is parallel to and has half the length of the third side? I'm going to try this one some more before I look for the answers, but please give me some guidance for both of them!
  2. jcsd
  3. Jun 29, 2004 #2
  4. Jun 30, 2004 #3
    Figured it out!

    If z=0, then you have the XY plane. So, find what T value makes z zero (2 in this case).
    Then, plug in 2 for t in x and y (you get 9 and 23 respectively). Thus, the point it intersects the XY plane is (9,23,0).

    That feels good!
  5. Jun 30, 2004 #4


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    Make it so that a points upwards and right, make b point down and right, and make c = a + b. You know the line segment joining the midpoints is:
    (1/2)a + (1/2)b
    = (1/2)(a + b)
    = (1/2)(c)... Q.E.D.

    For the first one, I'm not sure what you're referring to by "the co-ordinate plane," but you seem to have gotten that one, so you're fine.
  6. Jun 30, 2004 #5
    Scuse me akg! It should have been Coordinate Planes =p mb

    But, wouldn't c = a - b if a points upright and b points downright?
  7. Jul 1, 2004 #6
    Not if you define c as a + b!

  8. Jul 1, 2004 #7


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    Nope, it would be as I wrote it. Think about it: start at the "starting point" of a, and go in the direction that it goes in. Now, since you're adding b, you then proceed in the direction that b goes in, which is down. In this process you will have started at the "start" of c and ended at the "end."
  9. Jul 1, 2004 #8
    Ok, I get it. If a points downleft and b points downright, then c is b-a . Is this correct sir?

    Btw, thanks for your help akg and cook!
  10. Jul 1, 2004 #9


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    Yes, that's correct.
  11. Jul 1, 2004 #10
    Vectors are incredibly powerful. I've taken 4 classes of multivarient calc so far, and my knowledge of math increased exponentially!
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