# vector fields

• Nov 19th 2012, 11:24 AM
upanddown
vector fields
Hello, I'm having trouble understanding work done by vector fields following a specific path. Here's a specific question I'm stuck on from my homework:

Find the work done by the force field F = ⟨x sin y , y⟩ on a particle that moves along the parabola y = x^2 from (−1,1) to (2,4).

thank you!
• Nov 19th 2012, 11:46 AM
RBowman
Re: vector fields
Hi upanddown.

I write on paper faster than typing LaTeX with an iPad. So here's a photo.

Attachment 25807

Hope this helps.
• Nov 19th 2012, 11:55 AM
upanddown
Re: vector fields
wow thank you!! this helped a whole lot. I was setting my t bound to the y values and not the x values which was giving me the wrong answer.
• Nov 19th 2012, 12:01 PM
RBowman
Re: vector fields
No problem. It was fun working one of those. Hadn't done one in a long time.
• Nov 19th 2012, 01:06 PM
upanddown
Re: vector fields
so if the vector r is already parametrized, how do I know how to parametrize the vector F?

for example, the vector <x,-y> if I already know r=<t^2,t^3>
• Nov 19th 2012, 01:17 PM
upanddown
Re: vector fields
oh nevermind, I just figured it out. thank you anyways!