Find the divergence and curl of the vector A = rz sin ø ↑ + 3rz² cos o and evaluate both answers at coordinate point (2, 7, 1)

Q: Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t)…

A: Curve length problem..

Q: Find the divergence of the vector field F <7", 22°, zy* div F -

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Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…

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Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 1, – 5) for the funct 2x…

A: Given that  fx,y,z=ln2xy-z

Q: Evaluate a 3d divergence of 1/r^2 in the radial direction

A: V→=fr=r^r2∇·V→=1r2∂∂rr2·1r2         =0But above result is wrong. Because when we see flux in…

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: 1. Given the time_Varying position Vector X iat+j bf2+Kct 3 where ast,b=2,andc=3_are Cnstants. Find…

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Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: V=(x^2)yi-xyj+xyzk

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Find the gradient vector field of f бу f(x, у, 2) = X COS Z (бху) (6y бу -sin бх -sin бу i cos k…

A: Given,

Q: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

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Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Find the normal vector to the tangent plane of z = 4e"² - 6y at the point (12, 24, 4). x component y…

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Q: FIND THE DIVERGENCE OF THE VECTOR F GIVEN = sin (8x)i + cos (5y); + z ² k FIELD F(X, Y, 2) BY

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Q: (15) Find the divergence and curl of i = (ryz)î + (3x²y)ĵ + (æz² – y²z)& at point (2, –1,1).

A: Given v→=xyzi^+3x2yj^+xz2−y2k^ We have to find the divergence and curl of v→ at point 2,−1,1. If…

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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Q: Compute the vector line integral: x – 4 dx + (x – 4)² + y² -y dy :- 4)2 + y² where C is the circle…

A: To find the below vector integral. ∮C−yx−42+y2dx+x−4x−42+y2dy

Q: Find a vector parametrization of the circle of radius 3 in the xy-plane, centered at (4, -1),…

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Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: Find the normal vector to the tangent plane of z 7ea-2y at the point (4,8,7) x component = y…

A: The tangent plane is given as z=7ex2-2y and the point is (4,8,7) Let f(x,y,z)=7ex2-2y-z Then obtain…

Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Let the given vector field is :

Q: Find the divergence of the given vector field at point (1,1,1). Insert your answer below. Round to…

A: Fx, y, z=3x2yi+2xz3j+y4k Comparing with F=Pi+Qj+Rk, we get P=3x2y,  Q=2xz3,  R=y4 Now, ∂P∂x=∂3x2y∂x,…

Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

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Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

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Q: A curve in the xy-plane is defined by the vector valued function f(t)= (x(t), y(t)), d'y in terms of…

A: Given : x(t)=2ln(t)y(t)=2sin(-5t)   To find : d2ydx2

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

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: ☺ Find the unit fenpent and unit normal vectors to the space )curve (circulur helix) determined by…

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Q: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

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Q: Find the unit tangent vector T, the unit normal vector N, and the binormal vector B for curve r at…

A: Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any…

Q: The divergence of the vector G = i+ sin y j+ 3k is:- -8y -8y + siny + cosy x3 O 3,LI O 2,L y + siny…

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Q: Compute the unit binormal vector and torsion of the curve r(t) = (8t, 5 cost, 5 sint (5, 8 sint, -8…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

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Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

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Q: Consider the vector of electric field Е(х, у.2) %3 (sinh x)1 - (сosh y)) — хуг k a. Compute the…

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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence

A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…

Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

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Q: Compute the divergence and curl of the vector field cos (22 ) sin² (z² yz) 10 yz4 – xyz2 at the…

A: We have to find divergence and curl of vector field:

Q: Compute the unit binormal vector and torsion of the curve. r(t) = (11t, 5 cos t, 5 sin t) (5, 11 sin…

A: The given parametric equation is: rt=11t, 5cos t, 5sin t The unit binormal vector of the given curve…

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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