e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward unit normal vector with F = 3xî + 4y

Q: Find the unit tangent vector at the indicated point of the vector function r(t)=e^(18t) cos t…

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

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Q: Let C be the curve of intersection of the paraboloid a² + y² = z and the cylinder +(y-1)² = 1 (a)…

A: Given that C is the curve of intersection of the paraboloid x2 + y2 = z and the cylinder x24 + y -…

Q: Verify the validity of the Stokes's theorem for the vector A = e-bz sin ø a, + pe-bz , over the open…

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

A: Given:

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: Find the tangential and normal components of the acceleration vector. r(t) = cos(t) i + sin(t)j + tk…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: (d) Use Stokes' theorem to evaluate S. F.dr where = z²î + y²j + xk and C is the triangle with…

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Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

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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…

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Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

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-valued function, using the given parameter, to represent the intersection of the…

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Q: Let the position function of a particle be r = (t, t², 0). Find the normal component of the…

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Q: implement Stokes ' Theorem by taking the vector function Å = (x² + z)i + (y² + x)j+ (z² + y)k on the…

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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: Verify Stokes's theorem over a quarter circular disk with a radius, r = 4 in the 1* quadrant for any…

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Q: H.W: find vector parallel to the line of intersection between two planes. 1) x+y+z=1 and x+y= 2.

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Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

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Q: Consider the vector function $(t) = te“ i+ cos(t)j + k.Deter mine : a) ds/dt b)

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 2a² + 2y² and…

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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: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: For the vector function: r(1)=(Sf,21,5). find %3D (a) r'(t) and r'(4) vileuponi od yd bolbni PA pe…

A: The derivative of a vector function is obtained by differentiating all the components of that…

Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not…

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

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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: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: Let m be the mass of a metal rod that occupies the full length of the curve with vector…

A: Solve the given problem.

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

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

A: First solve the given equations for finding the values in terms of x

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

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: Let r(t ) = ti + cost j + t? k be a space curve. Which of the following vectors is parallel to the…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: Here we use the concept of gradient of a scalar function at given point.

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

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Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3t cos fi+ et sin…

A: We use the following formula to find the unit tangent vector T(t)=V(t)/|V(t)|

Q: Let r (t) = ti + e2t j + t³ k be a space curve. Which of the following vectors is perpendicular to…

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Q: Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

A: Given the curve  r→(t) = i→ + 2ln(t)j→ + 1tk→

Q: Determine the tangential (a,) and the normal (aN) components of acceleration of the vector function…

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Q: Let m be the mass of a metal rod that occupies the full length of the curve with vector…

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Q: Find the unit normal vector to the surface f(x,y) = y² – 4xy at (1,2). (a) i (b)- i (c) 8 i+4j (d)0…

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Q: Use Stokes theorem to evaluate: ∫∫Sc  n⋅(∇×F)dS, where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

A: Use Stokes theorem to evaluate:   ∫∫Sc n⋅(∇×F)dS,   where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

Q: ind a formula for a vector normal to the plane tangent to f(x,y) at (xo, Yo).

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Q: Let r (t) = ti + e2t j + t3 k be a space curve. Which of the following vectors is perpendicular to…

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Q: Find the flux F of through S, O 437 3 S F(x, y, z)=7zi-2j+yk, S: x+y+z=5, first octant O O 431 3 425…

A: