Math - Linear Algebra

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Let S be the plane defined by x−4y−3z = −18, and let T be the plane defined by −2x+8y+7z = 41. Find the vector equation for the line where S and T intersect.
x 0 0
y = 0 + t0
z 0 0

  • Math - Linear Algebra -

    1st one times 2
    2x - 8y - 6z = -36
    2nd
    -2x + 8y + 7z= 41
    add them
    z = 5

    sub into 1st x - 4y - 15 = -18
    x - 4y = -3
    x = 4y - 3
    let y = 0 , x = -3, z = 5 ---> point (0,-3,5)
    let y = 2 , x = 5, z = 5 ---> point (2,5,5)

    so direction of line of intersection is (2, 8, 0)

    using the point (2,5,5)
    x = 2 + 2t
    y = 5 + 8t
    z = 5

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