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(1 point) Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero Choose Choose v Choose (1 point) De...
point) Determine whether the line Integral of each vector field (n blue) along the semicircular, oriented...
point) Determine whether the line Integral of each vector field (n blue) along the semicircular, oriented path(in red is positive, negative of zero. LLLL Zero Negative : Positive Positive Positive (Click on a graph to enlarge it)
(1 point) Determine whether the flux of the vector field F through each surface is positive, nega...
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
Determine whether the work done by the force field is positive, negative or zero
Problem 13 Determine whether the work done by the force field is positive, negative or zeroa) [1 point] Positive. Negative. Zero (see above, circle one) b) [1 point] Positive. Negative. Zero (see above, circle one) c) [1 point] Positive. Negative. Zero (see above, circle one)
For each line, determine whether the slope is positive, negative, zero, or undefined. Line 1 Line 2 Line 3 Line 4 O...
For each line, determine whether the slope is positive, negative, zero, or undefined. Line 1 Line 2 Line 3 Line 4 O Positive O Negative O Zero O Undefined O Positive ON gative ero undefined O Positive O Negative O Zero Undefined O Positive O Negative O Zero O Undefined
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...
(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...
(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 field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2
(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...
An object moves though a vector field.
1. ( 8 points) An object moves though a vector field, \(\overrightarrow{\mathbf{F}}(x, y)\), along a circular path, \(\overrightarrow{\mathbf{r}}(t)\), starting at \(P\) and ending at \(Q\) as shown in the graph below.(a) At the point \(R\) draw and label a tangent vector in the direction of \(d \overrightarrow{\mathbf{r}}\).(b) At the point \(R\) draw and label a vector in the direction of the vector filed, \(\overrightarrow{\mathbf{F}}(R)\).(c) At the point \(R\) is \(\overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\mathbf{r}}\) positive, negative, or zero? Circle the correct...
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>....
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Question 6 Determine the line integral along the straight line c from point A to d. Find the para...
Question 6 Determine the line integral along the straight line c from point A to d. Find the parametric form of the line C. Use the vector field: Use the following values: a 1-0; a2-3; and a3-1: a-7; b-4: d-1; and θ-42 degrees.
Question 6 Determine the line integral along the straight line c from point A to d. Find the parametric form of the line C. Use the vector field: Use the following values: a 1-0; a2-3; and a3-1:...
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>....
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral scv. dr along the curve r(t) = <vt, t - 4,t +1> for Osts 4.[10]
point) Determine whether the line Integral of each vector field (n blue) along the semicircular, oriented path(in red is positive, negative of zero. LLLL Zero Negative : Positive Positive Positive (Click on a graph to enlarge it)
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
Problem 13 Determine whether the work done by the force field is positive, negative or zeroa) [1 point] Positive. Negative. Zero (see above, circle one) b) [1 point] Positive. Negative. Zero (see above, circle one) c) [1 point] Positive. Negative. Zero (see above, circle one)
For each line, determine whether the slope is positive, negative, zero, or undefined. Line 1 Line 2 Line 3 Line 4 O Positive O Negative O Zero O Undefined O Positive ON gative ero undefined O Positive O Negative O Zero Undefined O Positive O Negative O Zero O Undefined
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...
(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 field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2
(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...
1. ( 8 points) An object moves though a vector field, \(\overrightarrow{\mathbf{F}}(x, y)\), along a circular path, \(\overrightarrow{\mathbf{r}}(t)\), starting at \(P\) and ending at \(Q\) as shown in the graph below.(a) At the point \(R\) draw and label a tangent vector in the direction of \(d \overrightarrow{\mathbf{r}}\).(b) At the point \(R\) draw and label a vector in the direction of the vector filed, \(\overrightarrow{\mathbf{F}}(R)\).(c) At the point \(R\) is \(\overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\mathbf{r}}\) positive, negative, or zero? Circle the correct...
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
Question 6 Determine the line integral along the straight line c from point A to d. Find the parametric form of the line C. Use the vector field: Use the following values: a 1-0; a2-3; and a3-1: a-7; b-4: d-1; and θ-42 degrees.
Question 6 Determine the line integral along the straight line c from point A to d. Find the parametric form of the line C. Use the vector field: Use the following values: a 1-0; a2-3; and a3-1:...
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral scv. dr along the curve r(t) = <vt, t - 4,t +1> for Osts 4.[10]
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