Calculus

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5. Determine an equation for the plane that is exactly between the points A(-1, 2, 4) and B(3, 1, -4).

  • Calculus -

    vector AB must be the normal to the plane
    vector AB = (4,-1,-8)

    so the plane must have equation:
    4x - y - 8z = c
    but the midpoint of AB must lie on it, and that midpoint is (1, 3/2, 0)
    sub it in ...

    4 - 3/2 - 0 = c
    c = 5/2

    plane equation:
    4x - y - 8z = 5/2 or in only integers
    8x - 2y - 16z = 5

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