# Vector problem

1. May 10, 2014

### dk_ch

1. The problem
if {\vec{V}=ky\hat{i}+kx\hat{j} find the equation of the path

2. May 10, 2014

### haruspex

You need to show your attempt, or at least describe your thinking.

3. May 10, 2014

### HallsofIvy

What do "x" and "y" represent here? If they are two independent variables this is surface not a path.

4. May 10, 2014

### BiGyElLoWhAt

are you dealing with parametric equations?

5. May 10, 2014

### dk_ch

I wrote vel components separately as dx/dt and dy/dt . then the relations were integrated to have two equations relating x,y and t. Finally i eliminated t to get the equation. was i right?

i got eq (1) x = kyt +c1 and eq (2) y = kxt+c2
and final eq was (x-c1)/(y-c2)=y/x

Last edited: May 10, 2014
6. May 10, 2014

### dauto

Well that solution is not correct is it? Just differentiate it to check with the original equation (making sure to use the product rule) and you will see that.

7. May 10, 2014

### haruspex

y and x are functions of t, so you cannot integrate y with respect to t and get yt.
I would start by getting out of vectors and represent the equation as two simultaneous scalar differential equations. Then you can eliminate one dependent variable to obtain a second order ODE.
There may be neater ways.

You will also need to known the position at t=0.

Last edited: May 10, 2014
8. May 10, 2014

### dk_ch

thanks , I had doubt .
May I do it as follows .
dx/dt =ky and dy/dt=kx hence dx/dy=y/x or xdx=ydy .now by integrating we can get the result as y^2=x^2+ constant. .