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.(adsbygoogle = window.adsbygoogle || []).push({});

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) = arccos( (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.

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# Homework Help: Find the angle between vectors r(t) and r'(t) Question?

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