Vector analysis: show the object moves on the elliptical path

[manimaran1605]

Homework Statement

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

Homework Equations

(x/a)^2+(y/b)^2=1

The Attempt at a Solution

I tried the problem by changing cosωt=x and sinωt=y but i don't know how to proceed further, i don't know how to eliminate the unit vectors i, j. help me. Thank you

 

[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?

 

[HallsofIvy]

Homework Statement

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

Homework Equations

(x/a)^2+(y/b)^2=1

The Attempt at a Solution

I tried the problem by changing cosωt=x and sinωt=y

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.

but i don't know how to proceed further, i don't know how to eliminate the unit vectors i, j. help me. Thank you

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