Find the flux of the field F = x i + y j + z k across the sphere x2 + y2 + z2 = a2 in the direction away from the origin.

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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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: F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?

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Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

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 F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point…

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Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Compute the flux of the vector field - 5yi + 3j- 5azk through the surface S, which is the surface y…

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Q: Find the upward flux of F= (14e2,-7e²,-6) through the first-octant part of the triangle a+2y+3z-6.…

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