Use Stokes's Theorem to evaluate EF. dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with vertices (9, 0, 0), (0, 9, 0), (0, 0, 9)

Q: Given the inner product space (R³(R),+,.,-), where oy = 3x₁₁ + 2(x₂₁ + X₁3₂) + 3x₂y₂ + 2X3Y3, X =…

A: This is a problem related to inner product space. Please see the next step for details.

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

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Q: The plane 7= [1,0,0]+t[1,1,1]+s[L,−1,1]; s,t €R contains the point (3,0, p). Find the value of p.

A: Given r=(1,0,0)+t(1,1,1)+s(1,-1,1)

Q: 3. The point (1, k, 4) lies on the plane [x, y, z] = [1, 2, 0] + s[3, 0, 1] + t[2, −1, 1]. Find the…

A: Given point (1,k,4) is on plane.plane  is

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 √(-2¹ - 122³ - 30x²…

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Given u = (-5,0) and v = (-8, 7), find the projection of u onto v. Round to two decimal places, if…

A: The given vectors are The objective is to find the projection of u onto v.

Q: Consider two lines with parametric equations p(t) = (1, −4, −3) + t(−4, 3, 0) and q(t) = (−3, 3, −1)…

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Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

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Q: The cosine of the acute angle e between the diagonais of a quadriateral having vertices at (0,0,0),…

A: Given:

Q: Q7. a) Consider the vectors u , v and w are defined by u = i+j ,v = i+ 4j and w = 4i – 3j i. If the…

A: Given :

Q: 25 Given the points A(1;-2), B(3;0) and C(1;2) of the system (0; i). 1° Write a cartesian equation…

A: Question: Given points A1;-2,  B3;0 and C1;2 of the system O;i,j (1) Find the cartesian equation of…

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: let R = (1, 4, 3). RÓ has components (4, 1, 1), and Find the point Q such that v = sketch v.

A: Given: The components of vector v=RQ⇀ and  R= (1,4,3)  To find  Q and sketch v

Q: Q4 Evaluate S SR (x + 2y) dA where R is the triangle with the vertices (0, 3).(4, 1) and (2,6) using…

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Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: ind the egu. f Plane Passes through the Paints A(I,1-1) B(2,0 2) and C (0,-2,1) ? 7x-5५-१Z-6 ans.

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Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: Find polar coordinates with positive r and 0s 0 < 2n for each of the four points. (x, V) = (,8 (a)…

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Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Calculate the cross product. (i - 9j + 6k) x (j – k)

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Q: Evaluate ef zy³dx. ry³dx + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,5), and…

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Q: QUESTION 5 Calculate F.dr if F=(sinx,x²y³) and C is the triangle oriented counterclockwise with…

A: Solution is given below

Q: Evaluate F.dr where F(x, y) = xy i+ej and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: Consider the given information. Fx,y=xyi+exj and the line segment is from 2,0 to 4,0. Now, write the…