(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the triangle ABC whose vertices have position vectorsa,b, andcrespectively.

http://img106.imageshack.us/img106/4240/vectorat6.png [Broken]

Find the position vector of

(a) P, the mid-point of AB

(b) Q, the point of trisection of AB, with Q closer to B.

(c) R, the mid-point of the median CP.

2. Relevant equations

None really. It just seems that I have a major conflict with the textbook answer and I'm not quite sure why. The textbook says:

(a) ½(b+a)

(b) ⅓(2b+a)

(c) ½(a+b+c)

3. The attempt at a solution

(a) I got this answer. Looking at the diagram, if we theoretically add OB and OA tip-to-tail, the half of the resultant vector should give us OP.

(b) Similarly to (a),

AB =b+a

OQ = ⅓AB

--> OQ = ⅓(b+a)

I don't see whybis multiplied by 2.

(c) First off:

CP = CO + OP

CP = -c+ ½(b+a)

Then,

OR = OC + ½CP

OR =c+ ½(-c+ ½(b+a))

OR = ½c+ ¼b+ ¼a

Yeah, I don't see why my answers disagree with the textbook.

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# Triangle Vector Problem

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