Re: vector function question

Have you read the question correctly? What's the reference? The statement should be that 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 you can get as close to 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

you can get as close to

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.