Question

Express (3x+2y)i+(4x+9y)j as the sum of a curl free vector field and a divergence free vector field

Answer 1

@Jemurray3 can u help me?

Answer 2

F=CurlG+divH

Answer 3

and if i am not mistaken curl G must equal 0

Answer 4

Hi there. If you're working in two dimensions, a curl free vector field has the following form:
\[ \vec{F} = f(x)\vec{i} + g(y)\vec{j} \]
and a divergence free vector field has the form
\[ \vec{F} = f(y)\vec{i} + g(x) \vec{j} \]
Does that help at all?

Answer 5

Ya that helps

Answer 6

Thanks

Answer 7

hmm but there are other steps idk. maybe i will just google them

Answer 8

Btw long time no see. Its great to see u around again

Answer 9

Yeah, I've been away for awhile. Thanks. And what I mean is that vector field can be expressed as
\[ \left( 3x\space \vec{i} + 9y\space \vec{j} \right) + \left( 2y\space \vec{i} + 4x\space \vec{j} \right) \]
the first of which is curl-free and the second of which is divergence-free.

Answer 10

yes that is the answer but how did u get it?

Answer 11

ohhhh i get it I am sooo dumb sorry I quickly skimmed ur first explanation and the formula was staring right in my face hahahah thanks

Answer 12

That was awesome. Thanks :DDDDDDDDD

Answer 13

Sure, no problem