# Vector analysis

1. May 24, 2014

### manimaran1605

1. The problem statement, all variables and given/known data
problem form div curl grad and all that by h.m.schey
An object moves in xy-plane in such a way that its position vector r is given as a some function of "t" by

r= i acosωt+j bsinωt

show the object moves on the elliptical path
2. Relevant equations
(x/a)^2+(y/b)^2=1

3. The attempt at a solution
I tried the problem by changing cosωt=x and sinωt=y but i dont know how to proceed further, i dont know how to eliminate the unit vectors i, j. help me. Thank you

Last edited: May 24, 2014
2. May 24, 2014

### CAF123

You have to show that for the given parametrisation of the coordinates $x(t)$ and $y(t)$, the equation for an ellipse is satisfied, that equation being the one you wrote in Relevant equations. What is x(t) and y(t) in this case?

3. May 24, 2014

### HallsofIvy

Well, that's your first error. It should be x= a cos(ωt), y= b sin(ωt) so that x/a= cos(ωt), y/b= sin(ωt). Now use the fact that sin^2+ cos^2= 1.

?? There are no vectors in your equation for x and y as functions of t!

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