(d) Use Stokes' theorem to evaluate S. F.dr where = z²î + y²j + xk and C is the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1). The unit vector normal is upward.

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Q: 5. Using Stokes' theorem, find I (VxF) ndo, where F yi+xj+(y+z) k and S is the portion of the…

A: We have to find I=∫∫S∇×F·ndσ using Stokes' theorem.

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Q: Consider the plane: 2.x + 2y + z = 3 Find a unit normal vector.

A: Answer

Q: Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)

A: To find the unit normal vector to the surface x3-xyz+z3=1 at the point 1, 1, 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: 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: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

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Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

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Q: Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B…

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Q: (b) Verify your answer in (a) using Stokes' theorem, where the normal vector to the surface has a…

A: We have to apply Stoke's theorem.

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: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

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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: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

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

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Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

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Q: 2. Find a unit normal vector to the surface x + y +2 = 5 at the point (0, 1, 2). Ans. Û + 2k)

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Q: 2. Consider the curve traced out by the vector valued function r(t) = (sin t cos t, cos? t, sin t)…

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Q: 1. Compute ff,(V × F) - dS, where S is given by r² + y? + (z – 1)? = 2 and z > 0, and F(x, y, z) =…

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Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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Q: A normal vector to the tangent plane for the surface a y"z* = 1 at the point (1, 1, –1) is: %3D…

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Q: 1. Compute ff(V × F) - dS, where S is given by r² + y²+ (z – 1)² = 2 and z > 0, and F(r, Y, z) =…

A: Given: S is given by x2+y2+z-12=2  and z≥0 Fx,y,z=-esinzy,x+sinz,cosx

Q: The motion of a particle on an orbit defined by the vector equation is considered R(t) = (sin t-tcos…

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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 fur 5x…

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Q: Find the principal unit normal vector N for the curve r(t). r(t) = (3 + t)i + (7 + In(cos t))k, -1/2…

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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 =…

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Q: The scalar component of a vector A normal to cylindrical surface of radius 2 at point p A = p'a, +…

A: Given that, A=pBAap+sinϕaϕ+2zaz And the cylinder  surface of radius 2 is, p=2p-2=0 Now the normal…

Q: 7. The magnitude of the normal vector t, xt for a sphere of radius a in parametric form where u = p…

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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…

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Q: Which of the following is a normal vector to the tangent plane to the surface defined by f(x, y) =…

A: To determine a normal vector to the tangent plane to the surface defined by f(x,y)=10-x2-y2 at the…

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: Let C be the portion of the parabola y = x², oriented from the starting point (0,0) towards the end…

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Q: 5. Find the unit tangent vector, the unit normal vector and the binormal vector to the curve r(t) =…

A: The given vector curve is:  r→(t)=t3,t2,t Given point is: (1, 1, 1). Therefore t = 1. Now the Unit…

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: Find a unit normal vector to the surface f(x,

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

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

A: Stokes theorem is used to evaluate integration

Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: 4. Use Stokes Theorem to find the circulation of the vector tield F around any smoo th, Simple…

A: Stokes theorem ∫CF.dr→=∫∫Scurl F.N→ ds Curl of the vector point function Ff1, f2 f3…