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Plane Triangular Surface and Stokes' Theorem

4. Consider the plane triangular surface formed by the intersection of the plane x/A + y/B + z/C = 1 (A, B, and C all positive), with outward pointing normal, ie the normal pointing away from the origin.

Verify Stokes' Theorem for the vector field F = (x + y) + (2x − z) + (y + z) by performing the surface integral and line integral separately. Clearly show the surface and the positive direction of the line integral on a sketch.

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The surface is that of a triangle with vertices (a, 0, 0) ...

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Plane Triangular Surface and Stokes' Theorem are investigated.

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