Question
In: Advanced Math
Give examples–a formula and an illustration–of two-dimensional vector fields F⃗(x,y) with each of the following properties....
Give examples–a formula and an illustration–of two-dimensional vector fields F⃗(x,y) with each of the following properties. You could do the illustrations by hand.
a) The direction of F⃗ is constant but the magnitude is not constant.
b) The magnitude |F⃗| is constant but the direction is not constant.
c) All the vectors F⃗ along a horizontal line are equal, but F⃗ is not constant overall.
d) F⃗ (x, y) is perpendicular to xˆi + yˆj at every point (x, y).
e) F⃗ is a force field which repels from the origin. It is strongest near the origin, and weaker farther
away.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Give 2 different examples of an infinite dimensional vector space and provide an explanation in possible....
Give 2 different examples of an infinite dimensional vector
space and provide an explanation in possible.
This is a review question for linear algebra and I am trying to
better understand the concept.
Thank you!
Use the divergence theorem to calculate the flux of the vector field F⃗ (x,y,z)=−5xyi⃗ +2yzj⃗ +4xzk⃗ through...
Use the divergence theorem to calculate the flux of the vector
field F⃗ (x,y,z)=−5xyi⃗ +2yzj⃗ +4xzk⃗ through the sphere
S of radius 2 centered at the origin and oriented outward.
∬SF⃗ ⋅dA⃗ =
In a two-dimensional Cartesian coordinate system the y-component of a given vector is equal to that...
In a two-dimensional Cartesian coordinate system the y-component
of a given vector is equal to that vector's magnitude multiplied by
which trigonometric function, with respect to the angle between
vector and y-axis?
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In the previous question, what is the marginal rate of
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Efia enjoys both boba tea...
For each of the following vector fields F, decide whether it is conservative or not by...
For each of the following vector fields F, decide whether it is
conservative or not by computing curl F. Type in a potential
function f (that is, ∇f=F). Assume the potential function has a
value of zero at the origin. If the vector field is not
conservative, type N.
A. F(x,y)=(−14x−6y)i+(−6x+6y)j
f(x,y)=
C. F(x,y,z)=−7xi−6yj+k
f(x,y,z)=
D. F(x,y)=(−7siny)i+(−12y−7xcosy)j
f(x,y)=
E. F(x,y,z)=−7x^2i−6y^2j+3z^2k
f(x,y,z)=
For each of the following vector fields F , decide whether it is conservative or not...
For each of the following vector fields F , decide whether it is
conservative or not by computing curl F . Type in a potential
function f (that is, ∇f=F). If it is not conservative, type N.
A. F(x,y)=(10x+7y)i+(7x+10y)jF(x,y)=(10x+7y)i+(7x+10y)j
f(x,y)=f(x,y)=
B. F(x,y)=5yi+6xjF(x,y)=5yi+6xj
f(x,y)=f(x,y)=
C. F(x,y,z)=5xi+6yj+kF(x,y,z)=5xi+6yj+k
f(x,y,z)=f(x,y,z)=
D.
F(x,y)=(5siny)i+(14y+5xcosy)jF(x,y)=(5siny)i+(14y+5xcosy)j
f(x,y)=f(x,y)=
E. F(x,y,z)=5x2i+7y2j+5z2k
For each of the following vector fields F , decide whether it is conservative or not...
For each of the following vector fields F ,
decide whether it is conservative or not by computing curl
F . Type in a potential function f (that is,
∇f=F). If it is not conservative, type N.
A. F(x,y)=(−4x+5y)i+(5x+16y)j
f(x,y)= ?
B. F(x,y)=−2yi−1xj
f(x,y)= ?
C. F(x,y,z)=−2xi−1yj+k
f(x,y,z)= ?
D. F(x,y)=(−2siny)i+(10y−2xcosy)j
f(x,y)= ?
E. F(x,y,z)=−2x2i+5y2j+8z2k
f(x,y,z)= ?
Note: Your answers should be either expressions of x, y and z
(e.g. "3xy + 2yz"), or the letter "N"
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The children of an x-node are y-nodes
The children of a y-node are x-nodes
Each type of node uses a different comparison to order points.
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