Extremely Hard Calc II question (vectors)?

I've tried everything, and I can't get this problem. Can someone help? Its really hard, but i'd appreciate it =D.


This is supposed to be solved using vectors, but I couldnt make the symbol for vectors. Hopefully you can understand it...





http://img254.imageshack.us/my.php?image...


D is the midpoint of AC and E is BC such that BE:EC=1:t, where t%26gt;0. Let DE:EF=1:7 and vector AD= vector a and vectorAB=vector b


a) i. Express vector AE in terms of t, vector a, and vector b.


ii. Express vector AE in terms of vector a and vector AF


iii. Show that vector AF= [vector a(9+7t)/(1+t)] + [vector b(8t)/(1+t)]


b). i. Suppose that A, B, and F are collinear.


i. Find the value of t.


ii. It is given that ||a||=3 and ||b||=2 and angle BAC=1/3, then find vector a • vector b


iii. Find AB • BC and AD•DE


iv. Does the circle passing through B, D, and C also pass through F? Explain your answer.

Extremely Hard Calc II question (vectors)?
We have, more or less,





AD = DC = a


AC = 2a


EC = tBE


EF = 7 DE


AB = b





AE = AB + BE = b + BE





Sorry. I just got started, and I'm already pretty bored here. :(





It would help if you did the first, easier parts yourself, and only asked about the later parts where you really get stuck.