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Determine an equation for the line parallel to 2x + 6y + 4z = 1 and contains the point P(3, 2, 1).

  • Calculus -

    I think you posted this before, and probably got no response.
    You asked for "the" line parallel to the plane
    2x+6y+4z = 1.
    There is no unique line.
    Think of the floor of your kitchen as 2x+6y+4z = 1 and you have a table whose top is parallel to the floor and contains the point (3,2,1).
    Laying down a ruler would be a line parallel to the plane and passing through the point.
    How many such positions could you choose ?

    a normal to your given plane is (2,6,4) or (1,3,2)

    so any vector whose dot product with the above normal would be parallel to the plane
    e.g. (-5,1,1)∙(1,3,2) = -5+2+3 = 0
    and (1,-1,1)∙(1,2,3) = 1-3+2 = 0 are just two such vectors

    let's take (-5,1,1)

    so the equation of one such line is
    x = 3 -5t
    y = 2 + t
    z = 1 + t

  • Calculus -

    thank you :)

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