Pregunta: Let F = (xy, yz, zx) be a vector field and S be the parametric surface (x, y, 4-x^(2) - y^(2)) where 0 <= x <= 1 and 0 <= y <= 1. Consider the orientation of S such that the normal vector has a positive k component. *(Mark all the correct statements)* O 1. The surface S is a portion of a paraboloid. O 2. The unit normal with positive k component at the point

Let F = (xy, yz, zx) be a vector field and S be the parametric surface (x, y, 4-x^(2) - y^(2)) where 0 <= x <= 1 and 0 <= y <= 1. Consider the orientation of S such that the normal vector has a positive k component. *(Mark all the correct statements)* O 1. The surface S is a portion of a paraboloid. O 2. The unit normal with positive k component at the point (0.5, 0.5, 3.5) is - 1/sqrt(3) i-1/sqrt(3)j + 1/sqrt(3) k O 3. The flux of F through S is 4.35 O 4. The unit normal to the surface S with positive k component at the point (0.5, 0.5, 3.5) is 1/sqrt(3) i + 1/sqrt(3)j + 1/ sqrt(3) k O 5. The unit normal with positive k component at the point (0.5, 0.5, 3.5) is (1/sqrt(3), 1/sqrt(3), 1/sqrt(3)) O 6. The flux of F through S is 4.3712 O 7. The surface S is a portion of a hyperboloid. O 8. The flux of F through S is 713/180 O 9. The unit normal to the surface S with positive k component at the point (0.5, 0.5, 3.5) is - 1/sqrt(3) i+ 1/sqrt(3)j + 1/ sqrt(3) k O 10. The surface S is a portion of an ellipsoid. Sea F = (ry, yz, zx) un campo vectorial y S la superficie parametrica (x, y, 4 - x² - y²) donde 0 ≤ x ≤ 1y0 ≤ y ≤ 1. Considerar la orientacion de S tal que el vector normal tenga componente k positiva. ☐ 1. La superficie S es una porcion de un paraboloide. 2. La normal unitaria con componente & positiva en el punto (0.5, 0.5,3.5)esi+k 3. El flujo de Fa traves de S es 4.35 4. La normal unitaria a la superficie S con componente positiva en el punto (0.5, 0.5, 3.5) es ¹ / ² + 3 + 1/3 k 5. La normal unitaria con componente positiva en el punto (0.5, 0.5, 3.5)es ( 1 1 6. El flujo de F a traves de Ses 4.3712. 7. La superficie S es una porcion de un hiperboloide. 8. El flujo de F a traves de Ses 70, 9. La normal unitaria a la superficie S con componente positiva en el punto (0.5, 0.5, 3.5) es // ² + / ³ + 1 k 10. La superficie S es una porcion de un elipsoide.