Hi everyone, i have a midterm exam tomorrow night (Thursday night) and i'm looking at problems in the section of the book to help myself prepare. Can anyone answer this question for me? I have attempted to answer this problem but without the answer i don't know if i'm right.
1. Find the angle theta between vectors r(t) and r'(t) as a function of t.
2. Sketch the graph of theta(t)
3. Find any extrema of theta(t).
4. Find any values of t which the vectors r(t) and r'(t) are orthogonal.
and they give vector r(t) = t^2 ii + t ij
And there are no typos, that's really what the question asks.
First off, i have NO idea what ii and ij mean, i'm assuming they just mean i and j?
So far i have r(t)= t^2 + t and r'(t)=2t+1 and r(t)*r'(t)=2t^3 +t
and
theta(t) = (2t^3 +t) / (sqrt(t^4+t^2) * sqrt(4t^2 +1) )
Can anyone confirm this is right or wrong? And basically from here i have no idea what to do to answer 2-4 of the problem. My teacher said there would be a problem just like this on my exam, so i REALLY need to see this problem done out so i know what to do.
Can someone do this one out for me? It's not a homework, i just need to see it done out step by step so i can follow it, along with the answer. I have until Thursday night, so PLEASE help asap, thanks!
PLEASE help, i'm desperate.
oops i meant to add arccos in the theta(t) function, but is it still right?
