1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Line intersecting plane