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Math Help - normal vector

  1. #1
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    normal vector

    Find an equation for the plane that contains the line with parametric equations
    x = -7 - 4 t
    ,
    y = -6 + 4 t
    ,
    z = -3 + 8 t
    and is parallel to the line with parametric equations
    x = 3 t
    ,
    y = -7 + 5 t
    ,
    z = 5 + 8 t
    . Find the the normal vector and the EquationOfPlane.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Since the lines are both parallel to the plane their cross product is perpindicular to the plane, and therefore is the normal

    N = (-4 i + 4j + 8k)x(3i + 5j + 8k)

    For a point in the plane use (-7,-6,-3)
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    Since the lines are both parallel to the plane their cross product is perpindicular to the plane, and therefore is the normal

    N = (-4 i + 4j + 8k)x(3i + 5j + 8k)

    For a point in the plane use (-7,-6,-3)


    Would the equation of the plane be -8*t^2-7,56*t^2-6,-32*t^2-3=0? Because the computer keeps marking this incorrect.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    The equation should involve x, y, and z --I have no idea what you are doing.

    Once you have N = a i + bj + ck

    Use a(x -x0) + b(y-y0) + c(z-z0) = 0

    to generate the eqn of the plane where (x0,y0,z0) is the known point
    Last edited by Calculus26; September 7th 2009 at 04:33 PM.
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  5. #5
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    Quote Originally Posted by Calculus26 View Post
    The equation should involve x, y, and z --I have no idea what you are doing.

    Once you have N = a i + bj + ck

    Use a(x -x0) + b(y-y0) + c(z-z0) = 0

    to generate the eqn of the plane where (x0,y0,z0) is the known point
    I'll tell you what im doing. I took the cross product of these two vectors:

    a := [-4*t,4*t,8*t];
    b := [3*t,5*t,8*t];


    Where do i get the values for the initial and final variable?
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  6. #6
    MHF Contributor Calculus26's Avatar
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    N = (-4 i + 4j + 8k)x(3i + 5j + 8k)


    you don't include the t

    N = -8 i +56 j -32 k

    you can factor out the -8 and use

    N = i -7j + 4k

    (x+7) - 7(y+6) + 4(z+3) = 0

    I'll let you finish
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