ANSWER :
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Use Stokes' Theorem to evaluate fF.dr where F = (x +92) i + (1x + y)j + (2y = z)k and C is the curve of intersection of the plane x + 3y +z = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.)
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
a) Draw a surface whose boundary in the curve C b) Use Stoke's Theorem to set up the alternative integral to Fodr Let C be the curve of intersection of the plane. X+2=6 and the cyclinder x² + y2 = 9. Where F(x, y, z)=<xy, 32, 7y) and C is the Curve of intersection of the plane X+Z²6 and the Cylinder x² + y2 =9 view as clockwise as above
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k (a) Find curl ?⃗ curl ?⃗ = (b) What does your answer to part (a) tell you about ∫??⃗ ⋅??⃗ where C is the circle (?−25)^2+(?−30)^2=1 in the xy-plane, oriented clockwise? ∫??⃗ ⋅??⃗ =∫CF→⋅dr→= (c) If C is any closed curve, what can you say about ∫C ?⃗ ⋅??⃗ ? ∫C ?⃗ ⋅??⃗ = d. Now let ? be the half circle (?−25)^2+(?−30)^2=1 in the ??-plane with ?>30, traversed from (26,30) to (24,30). Find ∫C ?⃗ ⋅??⃗ by...
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral, where F(x, y, z) = (x2z, cy, 22) and C is the curve of intersection between the plane x+y+z=1 and the cylinder ? + y2 = 9 oriented clockwise when viewed from above. (b) Sketch a graph of both the plane and cylinder with so that the intersecting curve is clear. 2) Find the parametric equations for C and use them to sketch a...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
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Problem #8: Use Stokes' Theorem to evaluate | F• dr where F = (x + 52)i + (6x + y)j + (7y - -)k and C is the curve of intersection of the plane x + 3y += = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8: Just Save Submit Problem #8 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #8 Your Answer: Your Mark:...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...