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

4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1 surface x + 6. and the plane x+2y- 3z =1 at the point (1,3,2). 2

Find the equation of the plane that contain point A(3,1,4) and line I given parametrically as T(L) = (2,-1,3)+L(1,3,1)