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theorem. Let S be the portion of the plane 2x + 3y + z = 4 lying between the points (-1, 1, 3), (2, 1,
theorem. Let S be the portion of the plane 2x + 3y + z = 4 lying between the points (-1, 1, 3), (2, 1, -3), (2, 3, -9), and (-1, 3, -3). Find parameterizations for both the surface S and its boundary dS. Be sure that their respective orientations are compatible with Stokes' from (-1, 1, 3) to (2, 1, -3) S , (t ) = (3, 0, -6) t E [0, 1) X from (2, 1, -3) to (2, 3, -9) S, (t ) = (0, 2, - 6) E [1, 2) X from (2, 3, -9) to (-1, 3, -3) S3(t) = (-3,0, 6) tE [2, 3) X from (-1, 3, -3) to (-1, 1, 3) SA(t ) = (0, 2, - 6) t E [3, 4) X boundary $ (u, V) = (u, v, u - 2u, - 3v) UE [-1, 2], VE [1, 3] X
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