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Lines and Planes in Space - HELP SOON!

  1. Sep 12, 2004 #1
    I am very confused regarding a few problems in Calculus III. Any help
    or
    hints to any of these would be greatly appreciated!!

    1.) Are lines L1 and L2 parallel?

    L1: (x-7)/6 = (y+5)/4 = -(z-9)/8;
    L2: -(x-11)/9 = -(y-7)/6 = (z-13)/12;

    The answer says that they are parallel, which I don`t understand. I
    know 2
    lines are parallel if their direction vectors are parallel, but in this
    case V1 = <6, 4, -8>, and V2 = <9, -6, 12>. So they are not multiples
    of
    each other and thus I didn`t think they are parallel. What am I
    missing?

    2.) Write an equation of the plane that contains both the point P and
    the
    line L:

    P(2,4,6);
    L: x = 7-3t, y = 3+4t, z = 5 + 2t;

    I know to write an equation of the plane you need a direction vector
    and a
    point. I tried using <-3,4,2> crossed with <2,4,6> as my normal vector
    and
    <2,4,6> as my (X0, Y0, Z0). But I got the wrong answer...

    3.) Find an equation of the plane through P(3,3,1) that is
    perpendicular
    to the planes x+y = 2Z and 2X + z = 10. If I take the cross product of
    the
    second 2 planes that would give me a vector parallel to the equation
    that
    I want to find, but I need a normal vector. What to do?

    4.) Find an equation of the plane that passes through the points
    P(1,0,-1), Q(2,1,0) and is parallel to the line of intersection of the
    planes x+y+z = 5 and 3x -y = 4.

    5.) Prove that the lines x -1 = 1/2(y+1) = z-2 and x-2 = 1/3(y-2) =
    1/2(z-4) intersect. Find an equation of the only plane that contains
    them
    both.

    Sorry for so many problems. But any help would be great! Thanks!
     
  2. jcsd
  3. Sep 12, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Look at L2. Are you sure you've got the right direction vector?
     
  4. Sep 12, 2004 #3
    okay, so it's <-9. -6. 12> Does it make a difference though?
     
  5. Sep 12, 2004 #4
    oh nm

    oh nevermind... that was a stupid question. I see it now. Got any suggestions on the other problems? :)
     
  6. Sep 12, 2004 #5
    You get -3/2 when you divide corresponding coordinates, any corresponding coordinates.
     
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