Let S be the equilateral triangle with vertices at (1, 0, 0), (0, 1, 0), and (0, 0, 1). At each point of S, let n be the unit normal 2 whose coordinates are positive. Suppose that F (x, y, z) = 3 . Evaluate ff F. ndS.

1.3 (3) The ABC triangle has the vertices A(-1, 3, 2), B(-1, 5, 2) and C(1, 5, -2). A) Demonstrates that the AABC is a rectangular. B) Calculates the measurement of the two acute angles.

Let P be the parallelogram with vertices (-1,-1), (1, -1), (2, 2), (0, 2). Compute ffpxy dA. P

et △ABC be a triangle in S^2 (the two-dimensional sphere). Let the dual point C'∈S^2 of C be defined by the following three conditions:(i) d(C' , A)=π/2(ii) d(C' , B)=π/2(iii) d(C' , C)≤π/2A' and B' are defined analogously. Thus we get a dual triangle △A' B' C'. More precisely, △ABC is a non-degenerate triangle, andit follows (you may assume) that △A' B' C' is too.(question) Are there triangles △ABC in S^2 identical to their own dual △A'B'C'?   I would be very thankful if you could provide some explanation with the steps, thank you in advance.