Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4), (2, 3, -10), and (-1, 3, -4). Find parameterizations for both the surface S and its boundary as. Be sure that their respective orientations are compatible with Stokes' theorem. from (-1, 1, 2) to (2, 1, -4) S,(t) tE [0, 1) from (2, 1, -4) to (2, 3, -10) S2(t) tE[1, 2) from (2, 3, -10) to (-1, 3, -4) S,(t) = tE [2, 3) from (-1, 3, -4) to (-1, 1, 2) s,(t) tE [3, 4) boundary Ф(и, v) uE [-1, 2], v E [1, 3] II

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A: A detailed solution is given below.

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