Another vector task to solve!

Status
Not open for further replies.
S

sky_tm

Junior Member level 1
Joined
Feb 15, 2006
Messages
15
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,262
vector 3

i) If \[F = y^2 i - 3x^2 j + yzk\], find \[\nabla XF\] and \[\nabla \bullet F\]

ii) Show that \[G = 2xy^3 i + (1 + 3x^2 y^2 )j\] is conservative vector field on the entire plane.

iii) Find a potential function \[\Phi \] so that \[\nabla \Phi = G\].
 

Re: vector 3

sky_tm said:
i) If \[F = y^2 i - 3x^2 j + yzk\], find \[\nabla XF\] and \[\nabla XF\]

ii) Show that \[G = 2xy^3 i + (1 + 3x^2 y^2 )j\] is conservative vector field on the entire plane.

iii) Find a potential function \[\Phi \] so that \[\nabla \Phi = G\].
Click to expand...

i) you mean
...find \[\nabla XF\] and \[\nabla F\]?

ii) If G=f1(x,y) +f2(x,y)j. Then that G is conservative is equivalent to
df2/dx=df1/dy
G indeed satisfies this requirement by a trivial checking;

iii) \[ \Phi =y + x^2 y^3\]
 

Status
Not open for further replies.

Similar threads

Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…