In a triangle ABC the point M is located on the side BC such that the ratio of

the lengths of the segments BM and MC is L,i.e., lBMl: lMCl= L.

Find the vectorAMgiven thatAB=bandAC=c.

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- Nov 13th 2009, 09:18 AMknuckles1234Finding a vector from the sides of a triangleIn a triangle ABC the point M is located on the side BC such that the ratio of

the lengths of the segments BM and MC is L,i.e., lBMl: lMCl= L.

Find the vector__AM__given that__A____B__=**b**and__AC__=**c**. - Nov 13th 2009, 12:37 PMGrandad
Hello knuckles1234Using the law of addition of vectors

$\displaystyle \vec{AB}+\vec{BC}=\vec{AC}$$\displaystyle \Rightarrow \vec{BC}=\vec{c}- \vec{b}$Grandad

$\displaystyle \Rightarrow \vec{BM}= \frac{L(\vec{c}- \vec{b})}{L+1}$

$\displaystyle \Rightarrow \vec{AM} = \vec{AB}+\vec{BM}=\vec{b} +\frac{L(\vec{c}- \vec{b})}{L+1}$$\displaystyle = \frac{\vec{b} +L\vec c}{L+1}$