Question

Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar field or a vector field:

A: curl f
B: grad f
c: div F
d: curl(grad f)
e:grad F
f: grad(div F)
g: div(grad f)
h: grad(div F)
i: curl(curl F)
j: div(div F)
k: (grad f) x (div F)
l: div(curl(grad f)))

Answer 1

A not
B yes
c not
d yes
e not and so on....

Answer 2

but how do you know that?

Answer 3

dude, curl is aplied to vectors
grad to scalars
div---vectors
check any physics book
nabla scalar = vector
nabla.vector = scalar (the point means dot product)
nabla x vaector = vector

so just see if your expression have any sence. For ex. you can,t aply nabla to vector

Answer 4

for example the last expression
l: div(curl(grad f)))
after gradf you get vector
u aplye curl to it, you get another vector
u aplye div to it you get scalar
So all operations went ok, it means expression is correct (meaningfull)

Answer 5

now help in my question, :)

Answer 6

http://openstudy.com/study?version=feed:get-live-help&referrer=mathematics&domain=none#/updates/4f7c8c78e4b09f22231b831f

Answer 7

got it?

Answer 8

yeah and sorry i don't know how to do your problem

Answer 9

but what does nabla mean?

Answer 10

and what is the result of them, curl of a vector gives you a vector? grad of a scalar gives you a scalar and div or a vector gives you a vector?

Answer 11

\[\Delta\] like this one, just up side down
Can't type it, :)

Answer 12

grad of a scalar gives you a vector
div or a vector gives you a vector

rest is right

Answer 13

so curl of a vector gives you a vector?

Answer 14

yes

Answer 15

so they all give you a vector