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(2) For the vector field f 2z(ri yi)(22)k use the definition of line integral to evaluate the line integral J f.dr along the helical path r-costi + sintj+tk, 0St (3) You are given that the vector fie...
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r,...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to ev...
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t)
(a) Find the flux of the vector field F=yi-xjtk across the...
Q4 please and thank you (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Conside...
Q4 please and thank you
(3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Consider the vector field F(x, y) -ryi - 2j (-Fii F2j) and let C be the closed curve consisting of three segments: the straight line from (0, 0) to (1,0) followed by the circular arc from (1,0) to (0,1) followed by the straight line from...
Please make it simple and clear to understand 3. A vector field is given by (a) Show that the vector field r is conserva...
Please make it simple and
clear to understand
3. A vector field is given by (a) Show that the vector field r is conservative. Then find a scalar potential function f(r,y,) such that r - gradf and f(0,0,0) 0 (b) By the result of (a) the following line integral is path independent. Using the scalar potential obtained in (a) evaluate the integral from (0,0,2) (where-y-0) to (4,2,3) (where -1,y 0,2) 4.2,3) J(0,0,2)
3. A vector field is given by (a)...
Please help! Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r,...
Please help!
Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r, y) 2ri + yj. (3) (5.2) Evaluate the line integral fe F dr, where F(r, y, 2) = (x + y)i + (y- 2)j+22k and C is given by the vector function r(t) = ti + #j+Pk, 0 <t<1 (4) costrt>, 0St<1 (5.3) Given F(r, y) = ryi + yj and C: r(t)=< t + singat, t (3) (a) Find a function f such...
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'...
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...
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5...
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5. Ie + 2
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0,...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a p...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t)
(a) Find the flux of the vector field F=yi-xjtk across the...
Q4 please and thank you
(3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Consider the vector field F(x, y) -ryi - 2j (-Fii F2j) and let C be the closed curve consisting of three segments: the straight line from (0, 0) to (1,0) followed by the circular arc from (1,0) to (0,1) followed by the straight line from...
Please make it simple and
clear to understand
3. A vector field is given by (a) Show that the vector field r is conservative. Then find a scalar potential function f(r,y,) such that r - gradf and f(0,0,0) 0 (b) By the result of (a) the following line integral is path independent. Using the scalar potential obtained in (a) evaluate the integral from (0,0,2) (where-y-0) to (4,2,3) (where -1,y 0,2) 4.2,3) J(0,0,2)
3. A vector field is given by (a)...
Please help!
Question 5 25 (5.1) Sketch some vectors in the vector field given by F(r, y) 2ri + yj. (3) (5.2) Evaluate the line integral fe F dr, where F(r, y, 2) = (x + y)i + (y- 2)j+22k and C is given by the vector function r(t) = ti + #j+Pk, 0 <t<1 (4) costrt>, 0St<1 (5.3) Given F(r, y) = ryi + yj and C: r(t)=< t + singat, t (3) (a) Find a function f such...
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...
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5. Ie + 2
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0,...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
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