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Vectors - Finding a point of intersection

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    The line L is parallel to the vector 3i - 2j -2k and passes through the point P (1,0,-1/2)

    find the point of intersection Q of the line L with the plane ∏

    x+y+z=2

    3. The attempt at a solution
    I'm completely stumped with this, don't know where to start... I thought maybe

    (x,y,z) = (1,0,1/2) + 2(3,-2,-2)
    = (7,-4,7/8)

    but it's wrong.. Where do I start?
     
  2. jcsd
  3. Apr 11, 2012 #2

    tiny-tim

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    welcome to pf!

    hi dimens! welcome to pf! :wink:

    hint: what is a parametric equation for L ? :smile:
     
  4. Apr 11, 2012 #3
    Thanks for the welcome, I'm probably gonna be on here a lot to help me get through university. Lol.

    Parametric equations:

    x=1+3t
    y=-2t
    z=1/2-2t
     
  5. Apr 11, 2012 #4

    tiny-tim

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    ok, now that has to coincide with the equation x + y + z = 2 …

    sooo … t = … ? :smile:

    (btw, is that 1/2 or -1/2?)
     
  6. Apr 11, 2012 #5
    x+y+z = 2...

    so...

    1 + 3t -2t +1/2 - 2t = 2
    -t=0.5
    t=0.5


    plug it back into the equation right?

    (x,y,z) = (1,0,1/2) + 1/2(3,-2,-2)
    (x,y,z) = (1,0,1/2) + (3/2, -1, -1)

    (5/2,-1,-1/2)

    ... Answers wrong though, it's meant to be...

    (-7/2,3,-5/2)
     
    Last edited: Apr 11, 2012
  7. Apr 11, 2012 #6
    My bad...

    x=1+3t
    y=-2t
    z=-1/2-2t

    x+y+z = 2

    ....


    1+3t -2t -1/2 -2t = 2
    t= -3/2

    (x,y,z) = (1,0,-1/2) + -3/2(3,-2,-2)
    (x,y,z) = (1,0,-1/2) + (-9/2,3,3)

    = (-7/2,3,5/2)

    I got it :) Cheers tiny tim. I think I learn a lot better when I'm discussing things and typing it out on here.
     
  8. Apr 11, 2012 #7
    continuing the question:

    find the angle the line L makes with the plane ∏ at the intersection point Q.

    a.b = |a||b| cos∅

    (3,-2,-2) (-7/2,3,5/2)

    ... a.b = -21.5
    |a| = sqrt(17)
    |b| = sqrt(27.5)

    ∅ = arccos (-21.5/sqrt(467.5))

    ... answer is wrong. Am I missing something?
     
  9. Apr 11, 2012 #8

    tiny-tim

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    that's the wrong line, it has nothing to do with the plane ∏ :redface:
     
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