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Calculus

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Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4

  • Calculus - ,

    We need the direction of their line of intersection....
    double the 2nd plane equation, then add that to the 1st

    x+2y-3z = -6
    6x - 2y + 4z = 8
    7x + z = 2
    z = 2-7x

    let x=1
    then z = -5
    back in the 1st
    1 + 2y + 15 = -6
    y = -11 -----------> point (1,-11,-5)

    let x = 0
    then z = 2
    back in 1st
    0+2y -6 = -6
    y = 0 ------------> point (0,0,2)

    direction vector of line of intersection of the planes = (1, -11, -7)

    so one such vector equation is
    r = (2,-1,7) + t(1,-11,-7)


    (the question should have said, "Find a vector equation...."
    since the answer I obtained is not unique)

  • Calculus - ,

    We need the direction of their line of intersection? That's all the question mentioned... so is that still the correct answer? :/

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