6) Given a hemisphere bounded by S,: z = /25 – x2 – y? and S2:z = 0.Find the outward flux of the vector field F(x,y,z) = x³1+ y³] +z³k across the surface S1, using Gauss theorem. Ans: 3750n

Q: b) Given the vector field F(x, y, z) = y² tan 2x i - (lnx) (sin z) j+ey k. Find i. div F ii. curl F…

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Q: Find the flux of the vector field V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Find the curl of the vector fleld F(z, y) = 9ye" i+2ejat the point (-2, 0). Enter an exact answer.…

A: F(x, y)=9y2 ex3 i +2x2 ey jcurl F→=∇×F→curl F→=ijk∂∂x∂∂y∂∂z9y2 ex32x2 ey0         =∂∂x(2x2…

Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: Consider the vector field given by F(x, y) = (6xy – 152 y)i + (3a? + 3y – 10a°y)j find a function…

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Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: Consider the vector field v(x) i-j+ 6k. a) Calculate fvo dr, where I is the straight line from…

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Q: You are given the scalar field = -7y. a) b) c) d) Calculate Vo. Vo =( Calculate V at the point p =…

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Q: Find the curl of the vector field F(x, y, z) = x²i – 3j + yz?k. curl F = z?k curl F = z2j curl F =…

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Q: Q.3) Graph the vector field F(x, y) = –yi. Find V.(F × G) where F(x, y, z) = xi – 3j+ zk and G(r, y,…

A: given vector field Fx,y=-yi^  graph of the vector field

Q: A. Find the flux of a vector field = 8x i + 6y j+ 2z k through the portion of the plane z = 7 where…

A: As per the guidelines, I am supposed to do the first question only. Kindly repost the second…

Q: Match each of the following three vector fields to one of the four vector fields graphed below (yes,…

A: To match : The given vectors to the given vector fields. (a) F( x, y) = 2y , 2x (b)  F( x, y) = x2 ,…

Q: find the curl for vector field F = y³i+ xyj – zk

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Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…