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Problems 11. If A=3x2y-y3x2, calculate gradient A at a point · (1,-2,-1) 2. If A x2yi-2xzi+2yzk,...
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(a) In cylindrical coordinates (2,6,2) the gradient of a scalar function (0, 0, 2) is given...
(a) In cylindrical coordinates (2,6,2) the gradient of a scalar function (0, 0, 2) is given by au 1 au au Vy= ap The divergence of a vector function ep + eo + pao ez az v(p, 0, ) = vp (2,0,ze, + vel,0,)e +v:(0,0,z)e, + θυ: az pa where Up, va, and v, are scalar functions, is given by 1 a i due V.v= (pup) + ρθρ' Let f(0, 0, 2) = e sin() + cos(0) (i) Calculate f....
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ betwe...
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ between the vectors a- 10i -j- 5k and b 2i+j- 21k Answer (in radians): θ Answer(s) submitted: (incorrect) 3. (1 point) Find a vector a that has the same direction as -6,5,6) but has length 3. Answer: a Answer(s) submitted: (incorrect) 4. (1 point) Suppose we...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
ems (1 point) A) Consider the vector field F(x, y, z) = (6yz, -7zz, zy). Find...
ems (1 point) A) Consider the vector field F(x, y, z) = (6yz, -7zz, zy). Find the divergence and curl of F. div(F) = V.F= curl(F) = V F =( ). 5 (5x?, 2(x + y), -7(x + y + x)) 7 B) Consider the vector field F(x, y, z) Find the divergence and curl of F. div(F) = V.P= curl(F) = V XF =( 8 9 10 )
Question 4 Consider the vector field F(,y)(r,y). (a) Calculate div(F) and curl(F). (b) Is F a gra...
Question 4 Consider the vector field F(,y)(r,y). (a) Calculate div(F) and curl(F). (b) Is F a gradient vector field? If yes, find f such that F= ▽ (c) Find a low line for F passing through the point r(1) (1,e) 3 4 5 6 8
Question 4 Consider the vector field F(,y)(r,y). (a) Calculate div(F) and curl(F). (b) Is F a gradient vector field? If yes, find f such that F= ▽ (c) Find a low line for F passing...
(1 point) If a = i +9j+ k and b = i +13j + k, find...
(1 point) If a = i +9j+ k and b = i +13j + k, find a unit vector with positive first coordinate orthogonal to both a and b. i + j + k
SunnmelauTo.pai 5/6 Question 4. Consider the veetor field F(r. y) (r2.y) (a) Calculate div( F) an...
sunnmelauTo.pai 5/6 Question 4. Consider the veetor field F(r. y) (r2.y) (a) Calculate div( F) and curl(F) (b) Is F a gradient vector field? If yes, find f such that F= ▽f (c) Find a flow line for F passing through the point r(1) (1.e)
sunnmelauTo.pai 5/6 Question 4. Consider the veetor field F(r. y) (r2.y) (a) Calculate div( F) and curl(F) (b) Is F a gradient vector field? If yes, find f such that F= ▽f (c) Find a...
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...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(a) In cylindrical coordinates (2,6,2) the gradient of a scalar function (0, 0, 2) is given by au 1 au au Vy= ap The divergence of a vector function ep + eo + pao ez az v(p, 0, ) = vp (2,0,ze, + vel,0,)e +v:(0,0,z)e, + θυ: az pa where Up, va, and v, are scalar functions, is given by 1 a i due V.v= (pup) + ρθρ' Let f(0, 0, 2) = e sin() + cos(0) (i) Calculate f....
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ between the vectors a- 10i -j- 5k and b 2i+j- 21k Answer (in radians): θ Answer(s) submitted: (incorrect) 3. (1 point) Find a vector a that has the same direction as -6,5,6) but has length 3. Answer: a Answer(s) submitted: (incorrect) 4. (1 point) Suppose we...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
ems (1 point) A) Consider the vector field F(x, y, z) = (6yz, -7zz, zy). Find the divergence and curl of F. div(F) = V.F= curl(F) = V F =( ). 5 (5x?, 2(x + y), -7(x + y + x)) 7 B) Consider the vector field F(x, y, z) Find the divergence and curl of F. div(F) = V.P= curl(F) = V XF =( 8 9 10 )
Question 4 Consider the vector field F(,y)(r,y). (a) Calculate div(F) and curl(F). (b) Is F a gradient vector field? If yes, find f such that F= ▽ (c) Find a low line for F passing through the point r(1) (1,e) 3 4 5 6 8
Question 4 Consider the vector field F(,y)(r,y). (a) Calculate div(F) and curl(F). (b) Is F a gradient vector field? If yes, find f such that F= ▽ (c) Find a low line for F passing...
(1 point) If a = i +9j+ k and b = i +13j + k, find a unit vector with positive first coordinate orthogonal to both a and b. i + j + k
sunnmelauTo.pai 5/6 Question 4. Consider the veetor field F(r. y) (r2.y) (a) Calculate div( F) and curl(F) (b) Is F a gradient vector field? If yes, find f such that F= ▽f (c) Find a flow line for F passing through the point r(1) (1.e)
sunnmelauTo.pai 5/6 Question 4. Consider the veetor field F(r. y) (r2.y) (a) Calculate div( F) and curl(F) (b) Is F a gradient vector field? If yes, find f such that F= ▽f (c) Find a...
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...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
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