(b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane z = 0. It is oriented by an outward unit normal vector with F = 3xî + 4yĵ – 5z²k.

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

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A: This is a greens theorem problem

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A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: calculate the flux of the vector field through the given surface F = zi + (y −1)j + 5xk, and S is…

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Q: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Determine the acceleration (vector and magnitude) of the fluid particle occupying the point (-2, 1,…

A: Accleration is given by  a→ =DV→Dt= ∂V→∂t+(V.→∇)V→Here, V→ =2xy i^+xz j^+yz k^Hence, ∂V→∂t= ∂2xy…

Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F= 6i+y4z8j-y…

A: According to the given information, it is required to find the flux of the vector field across the…

Q: Consider the paraboloid defined by x-4y2+4z2. (a) Which of the following vector-valued functions…

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Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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Q: Consider the ellipsoid 3x? + y? + z² = 11. The equation of the tangent plane to this ellipsoid at…

A: 3 x2 + y2+z2=11 and the point is (1,-2,-2)

Q: calculate the flux of the vector field through the given surface. ~F = ~i + 2x~j + 4y ~k, and S is…

A: GIVEN: F = i + 2xj + 4yk Surface, z = 2x2 + y + 3

Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid…

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Q: Find a vector function r(t) that describes the curve of intersection between the elliptical cylinder…

A: given, elliptical cylinder 4y2+z2=4  and the plane x+y=1 we have to find a vector function r(t) that…

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Q: 6. Given the space curve r(t) = (t, 2et, e2t), find the tangential and normal components of…

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Q: d the normal vector to the surface y = 16x at (4,8). (a) 16(f-j) (b) (1 – f) (c) 6(1 – 1) (d) none…

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Q: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

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A: Finding the Position Vector for a Particle: The integration of the acceleration vector is the…

Q: Determine the acceleration (vector and magnitude) of the fluid particle occupying the point (-2, 1,…

A: The acceleration vector is,                              a =ax + ay +az  where…

Q: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: disk

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Q: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: 19. Suppose that the normal unit vector N of a surface S at z = f(x, y) is determined, how does the…

A: Note: As company policy, we solve first question only. Please resubmit the rest of the questions in…

Q: Find a vector function, r(t), that represents the curve of intersection of the The cylinder x² + y2…

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

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Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

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Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

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A: position vector of a particle in the xy-plane is given by &lt; t^2+1, ln(2t+3) &gt; for all t&gt;=0

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: O Solve the electric flux through a paraboloid z =x² + y² – 16 that lies below plane z = 0. It is…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: We have to find vector function For this we have given equation of paraboloid and parabolic cylinder…

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

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Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

Q: A force F acts on a particle that is moving in the plane along the semi-circle parameterized by 7(t)…

A: Work done W=∫CF.ds=∫abF(r(t)) . r'(t)dt   Where curve C is given by parametric equation r(t)

Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…

A: Take dot product along limit of integration and integrate

Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

Q: A vector normal to the surface y-:-3 at the point (-1,-2, 2) is (a) i+2j+k (b)-i+j+2k) (e) (21 -j+k)…

A: The given surface is: xy-z=3 And, the given point is: -1, -2, 2 Since, the gradient represents a…

Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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