How Is the Vector Solution 1/2(p-q) Derived?

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The discussion revolves around deriving the vector solution 1/2(p-q) related to triangle PMQ. The user seeks clarification on how to express vector p in terms of vectors PM and MQ, and similarly for other related vectors. Daniel points out that in triangle PMQ, vector p can be expressed as the sum of vectors PM and MQ, while also noting that vector PM equals vector MR. The user is encouraged to combine the equations to arrive at the desired solution before an upcoming test. The conversation highlights the importance of understanding vector relationships in geometric contexts.
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Hi I was wondering if anyone could help me with this problem:

http://img209.echo.cx/img209/5105/vector5mm.png

In my textbook it says the answer is 1/2(p-q) but I don't understand how that answer is acheived. Any help would be appreciated.

Many thanks.
 
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Consider the triangle PMQ.Can u express \vec{p} in terms of \vec{PM} and \vec{MQ}...?

And the same for the other triangle...

What relation is there between \vec{PM} and \vec{MR} ?

Daniel.
 
In triangle PMQ \vec{p} = \vec{PM} + \vec{MQ}.

Also \vec{PM} = \vec{MR} as in they're the same distance. Could anyone explain how I get the answer please? As my test is now tomorrow :smile:
 
The way i see it

\left\{\begin{array}{c}\vec{MQ}+\vec{PM}=\vec{p}\\ \vec{MQ}+\vec{q}=\vec{MR} \end{array} \right

Now add the 2 eqns.

Daniel.
 

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