Question

1. Consider a fictitious cube region with dimension (1 m) (1 m)x(1 m). It is anchored at the spatial origin and point (1,1,1) m. All of its faces are parallel to the Cartesian axes, as shown in the figure below. Suppose a static vector field exists in the space, A(x, y, z) = x2 yzî + xy2 zý + xyz22. Please verify the Gauss's theorem, SS V. Adv = ffA.ds, where V is the cube region and S is the surface of the cube. -(1,1,1) meter Figure for Problem 1

Answer 1

solution dionension of cube (Im x 1mx1m) (2, 5,2). Wyzn + y2z g + hyzung Causs's the onam SSDR dr = HR. let's take first term JIE V. Pa = 15$ (2ny2 + 2732497 ya thay =ll. (anyz +222 +2242/dhana HA1 = 1 / (-27 228) + 1 T ady (-dna z ý) 4 Ilimo (-andge) + limo, koydz.) + T ahun 5) 60 Ila andy ² )

= 0 totot llpyzdy dat Inadh d2+ hydnas 111 V. CAS HAJI