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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: fredrick on October 12, 2008, 04:18:17 pm

Title: My attempt at a Vector Proof
Post by: fredrick on October 12, 2008, 04:18:17 pm: ABCD is a parallelogram. M is the midpoint of AB. P is the point of trisection of MD nearer to M. Prove that A, P,C are collinear and that P is a midpoint of trisection of AC.

Does this make much logical sense? anyhting i should alter?

[IMG]http://img152.imageshack.us/img152/5307/vectorproofsbm8.jpg[/img]
[IMG]http://img152.imageshack.us/img152/vectorproofsbm8.jpg/1/w757.png[/img]
Title: Re: My attempt at a Vector Proof
Post by: Ahmad on October 12, 2008, 04:47:30 pm: I only briefly skimmed through this, but it could be easier to follow by implementing a few adjustments, although apart from a few structural points I do think it works out.

Firstly, words are your friend. Words can often express things more easily than math symbols, especially to explain in broad terms what you're doing. You don't have to have many words (yuck!) just a few which gives the reader a sense of direction. For example, you could mention to the reader that it suffices to prove that $\vec{AP} = \frac{1}{3}\vec{AC}$ , which would prove both the collinearity of A, P and C, as well as that P trisects AC.

Secondly, you could structure your proof slightly better. For example, you said $\vec{AP} = k \vec{AC}$ but this assumes A, P, C are collinear, which is to be proved. It's not hard to fix this.

Lastly, don't take my criticism too harshly, I think overall this is a good try, better than I've seen by a lot of people. In particular I like the diagram. :)
Title: Re: My attempt at a Vector Proof
Post by: fredrick on October 12, 2008, 05:01:28 pm: ok i understand that so i should of just stopped when i showed AP=(1/3)AC which shows the collinearity and that it also trisects.