3.) (12 pts.) Find the Flux of the velocity vector field F(x, y) = (yº)i +...
can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
2.) (12 pts.) Consider the velocity vector field F(x, y) = (y)i - (c); (units: gm/(cm)(sec)). Find the Circulation (Flow) of Falong path C given in the diagram below. У C (90) (0,0) (1,0) Х
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
[25 pts) Let F(x, y, z) = x?i + xyj + zzk be a vector field in space. Let S be the open surface 2 = 25 -x2 - y2, which is the upper hemisphere (or dome) of radius 5. Calculate the flux integral ] F.N ds S
2. [25 pts) Let F(x, y, z) = x+i+ xyj + xzk be a vector field in space. Let S be the open surface z= 25 – x2 - y2, which is the upper hemisphere (or dome) of radius 5. Calculate the flux integral F.NDS
7.) (12 pts.) Verify Green's Theroem 2 for the Vector Field F(x, y) = (xy)i + (y?)3, where the closed curve C is the circle x² + y2 = 1.
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t) (a) Find the flux of the vector field F=yi-xjtk across the...
Please help me how to solve this problem Find the circulation of the vector field F(x, y) = P(x, y)i + Q(x, y)j where P(x, y) = [2 − y] / [9x^2 + (y − 2)^2] + [−2 − y / [9x^2 + (y + 2)^2] , Q(x, y) = x / [9x^2 + (y − 2)^2] + x / [9x ^2 + (y + 2)^2] , around the simple closed curve C = C1 ∪ C2, where C1 is...
Could you solve this problem? realted to vector field calculus Find the circulation of the vector field P(ar, y)i +Q(x, y)j F(ar,y) where 2-y P(x, y) = 9x2 + (y - 2)2 -2 y 9r2 + (y+ 2)?'| Q(x, y) = 9r2 + (y- 2)? * 9xr2 + (y + 2)2' around the simple closed curve C = Ci U C2, where C1 is the path along the line y = x from (-3, -3) to (3,3), and C2 is...