Re: vector function question

Have you read the question correctly? What's the reference? The statement should be that $\displaystyle \mathbf{r}(t)$ is part of a line through the origin; it doesn't have to be the entire line.

Re: vector function question

r(t) is the position vector. the question asks to prove that the particle's trajectory is a straight line through origin.

Re: vector function question

please someone just tell me the question has a typo because this is driving me a little nutty.

Re: vector function question

Quote:

Originally Posted by

**kkoutsothodoros** please someone just tell me the question has a typo because this is driving me a little nutty.

I have to see the question before I can decide if there's typo. In any event, what I think the question means is that the trajectory is a line through the origin, but doesn't include the origin. If you let $\displaystyle t\rightarrow -\infty$ you can get as close to $\displaystyle (0,0)$ as you like.

Re: vector function question

Quote:

Originally Posted by

**ojones** I have to see the question before I can decide if there's typo. In any event, what I think the question means is that the trajectory is a line through the origin, but doesn't include the origin. If you let $\displaystyle t\rightarrow -\infty$ you can get as close to $\displaystyle (0,0)$ as you like.

exact question as written in Richard A. Silverman's Modern Calculus and Analytic Geometry:

suppose the radius vector r (bold vector notation) = r(t) of a moving particle satisfies the differential equation dr/dt (bold vector r) = ar(t) where a is a scalart constant. Prove the particle's trajectory is a straight line through the origin.

I don't see how I've misinterpreted. But Silverman's books are good so I tend to trust.

Re: vector function question

There seems to be a small ommission in Silverman's question. The solution you found is correct and you're right in that it doesn't pass through the origin. The trajectory is a line through the origin but doesn't include the origin.