Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0), (1,0, 2), (1,3, 2), (1, 3, 0) oriented in the positive direction of x-axis.

Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

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Q: a Compute the flux of the vector field i = -2 i + 5j – 4 k through the rectangular region shown…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 3x2j -z2 k;…

A: F = 3x2 j -z2 k,y = 2x2,0≤z≤2,-1≤x≤1.

Q: The vector field F = ( , ,2²) has a scalar potential in the region R= {(r, y, z) E R³ : x> 0}

A: ANSWER: TRUE

Q: Find the work done by vector field F(x, y, z) = xi + yj + (x + z)k on a particle moving along a line…

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Q: Calculate the flux of the vector field of (xv.z = r-)i +0= 4xz) i +xzk across the box bounded by *=y…

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Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the…

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Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

Q: Compute the flux of the vector field F(x, y, z) = 5i + 5j+ 6k through the rectangular region with…

A: Given that, The vector field F→x,y,z=5i→+5j→+6k→ through the rectangular region with corners at…

Q: Consider the vector field F(x,y,z)=(7y,7x,2z). Show that F is a gradient vector field F=∇V by…

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Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

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Q: Find the flux of the field F =(x + y)i -(x2+y2)j outward across the triangle with vertices (1, 0),…

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Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

A: Outward flux by using gauss divergence theorem

Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

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Q: Compute the curl, V x F, of the vector field. F(x, y, z) = 7xi + 9yj + 2zk curl(F) = -7xi – 5yj +…

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Q: Compute the flux of the vector field F(x, y, z) = 6ỉ +3j + 2k through the rectangular region with…

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Q: Compute the flux of the vector field F = 2xi + 5yj through the cylindrical surface shown below, if a…

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Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Calculate the flux of the field F=xi+yj across the closed plane curve C, where C is the closed…

A: Given a field: F=x2i+y2j We need to find the flux of this field across a closed plane curve C which…

Q: Find the streamlines of the vector field and the streamline through the given point. F(x, y, z) =i+…

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Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: Find the flux of the field F(x, y, z) = (x, y, -2z) through the surface z = ! =1– 2² – y² (0 < ¤< 1,…

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Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

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Q: Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of…

A: Given vector field is  F=x2zi+y2zj+z3k              (i) Given surface is  x2+y2=16z=2z=-2 Let us…

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: The vector field F = (, i, 2²) has a scalar potential in the region R= {(x, y, 2) E R³ : r² + y? >…

A: We find out true or false.

Q: Compute the flux of the vector field F = 5xi + yj through the cylindrical surface shown below, if a…

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Q: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

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Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: Compute the flux of the vector field = 2 i + 5j- 5k through the rectangular region shown below,…

A: We have to find flux.

Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

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Q: Compute the flux

A: Compute the flux

Q: Compute the flux of the vector field i = -2i+ j- 2 k through the rectangular region shown below,…

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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: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: Find the flux of the vector field F = xi - 3y j - 2z k through the part of the plane 2.x + 3y + z =…

A: The given problem is to find the flux of vector field F through the part of the plane given in the…

Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…

Q: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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Q: Find the flux of the vector field J = 2x?yi + 4zj ou t of the closed box 0 < x < 2,0 < y< 8,0 < z <…

A: We have to find the flux

Q: Determine the flux of the vector field F = x³i – 2yĵ + 7z?k across a cone z = /x2 + y2 + 3 that lies…

A: Gauss theorem states that if V is a volume inclosed by a closed surface S then  flux=∫∫S F.n dS=∬∫V…

Q: Consider the vector field F(x, y, z) = (-2y, –2x, 8z). Show that F is a gradient vector field F = VV…

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Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…

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…

Q: Compute the flux of the vector field F = 2xi + 3yj through the cylindrical surface shown below, if a…

A: We have to compute the flux of the  given vector field.

Q: Compute the flux of the vector fieldi = -3 i+ 4j- 2 k through the rectangular region shown below,…

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Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

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