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) = 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.