Let S Be the Triangle with Vertices at (12,0,0), (0,6,0)and $x + 2 y + 2 z = 12$

question 47

Essay

Let S be the triangle with vertices at (12,0,0), (0,6,0)and (0,0,6), oriented outward (away from the origin).So S lies in the plane $x + 2 y + 2 z = 12$ .Let C be the oriented boundary of S.Evaluate $\int _ { c } \left( - \frac { 2 y } { 3 } \vec { i } - \frac { z } { 3 } \vec { j } - \frac { 2 x } { 3 } \vec { k } \right) \cdot d \vec { r }$ .

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