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Linear algebra, point of intersection

  1. Mar 7, 2009 #1
    1. The problem statement, all variables and given/known data
    1) x=3+t
    y=2-4t
    z=-5+11t

    2)12x+10y-4z

    Find the point where these two lines intersect.


    please help!!
     
  2. jcsd
  3. Mar 7, 2009 #2
    I mean, where the line in 1 and plan in 2 intersect
     
  4. Mar 7, 2009 #3
    Last edited by a moderator: Apr 24, 2017
  5. Mar 7, 2009 #4
    =48

    but I don´t think that matters
     
  6. Mar 7, 2009 #5
    It does matter. The equation 12x+10y-4z=48 defines a different (but parallel) plane then the equation 12x+10y-4z=0. For example the second one passes through the origin while the first does not (to see this, just check if x=0,y=0,z=0 satisfies the equation).
     
  7. Mar 7, 2009 #6
    okey thanks

    but do you know how to solve it?
     
  8. Mar 7, 2009 #7
    This is a system of linear equations (4 equations, 4 unknowns). I am almost sure you have solved systems of linear equations before, for example when intersecting two lines in the plane:

    2x+y=1
    x-3y=0

    How did you do that? Hint: Substitution. Your problem can be solved in a similar way.
     
  9. Mar 7, 2009 #8
    I really haven´t solved anything like this. I´m a beginner.
    I just really need a good teacher to show me how to do this.
    Can you? Or if you can´t solve it, can anybody else?
    And, the answer of the plane is =46, not 48.
     
  10. Mar 7, 2009 #9

    lanedance

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    Homework Helper

    you have an equation for a plane

    ax + by + cz = d
    a,b,c,d constants

    and a line (x(t),y(t),z(t))

    what happens when we are on both the plane & line? bothe equations will be solved

    substitute your line components (x(t),y(t),z(t)) into the equation of the plane & solve for t

    this give the point on the line in terms on twhere the plane & line intersect
     
  11. Mar 7, 2009 #10

    Dick

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    Science Advisor
    Homework Helper

    Put your expressions for x, y and z in terms of t into the equation of the plane. Then solve for t.
     
  12. Mar 8, 2009 #11
    Anyone who can show me some equations?
     
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