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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: kaanonball on January 13, 2009, 02:58:17 pm

Title: More Vector Proof Questions
Post by: kaanonball on January 13, 2009, 02:58:17 pm: The Question
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 and C are collinear and that P is a point of trisection of AC.

At the moment I'm not sure how to get started with this question, mainly because I'm unsure how to represent P is the point of trisection of MD nearer to M on the Parallelogram.

Also if vectors are collinear, does that mean for instance A = mP = nC ?
Title: Re: More Vector Proof Questions
Post by: /0 on January 13, 2009, 03:53:46 pm: "P is the point of trisection of MD nearer to M on the Parallelogram."

This means that $MP:PD = 1:2$ , or $MD = 3MP$

If points A, P and C are collinear, you prove that

$\vec{AP} = k\vec{AC}$

or

$\vec{AP} = k\vec{PC}$

In general for 2 dimensions, collinear vectors must be dependent and share a point.
Title: Re: More Vector Proof Questions
Post by: kaanonball on January 13, 2009, 10:42:47 pm: Oh ok, I get it now! Thanks. There's just one more thing how do I prove point P is the point of trisection?
Title: Re: More Vector Proof Questions
Post by: hamtarofreak on January 15, 2009, 02:56:44 pm: $3\vec{AP} = \vec{AC}$