Consider the vector field F(x,y,z) = xi + 3xzj + -2yk and the surface S which is the part of the plane x + 2y + z - 3 that lies in the first octant, oriented upward. Without making any calculations, is the flux through the surface positive or negative? Why? Calculate . What is the boundary dS of the surface? Set up and evaluate the line integral . Note that Stokes' Theorem applies. Which integral was easier to find?
Show transcribed image textConsider the vector field F(x,y,z) = xi + 3xzj + -2yk and the surface S which is the part of the plane x + 2y + z - 3 that lies in the first octant, oriented upward. Without making any calculations, is the flux through the surface positive or negative? Why? Calculate . What is the boundary dS of the surface? Set up and evaluate the line integral . Note that Stokes' Theorem applies. Which integral was easier to find?