Hello knuckles1234 Originally Posted by
knuckles1234 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 vector AM given that AB = b and AC = c.
Using the law of addition of vectors$\displaystyle \vec{AB}+\vec{BC}=\vec{AC}$
$\displaystyle \Rightarrow \vec{BC}=\vec{c}- \vec{b}$
$\displaystyle \Rightarrow \vec{BM}= \frac{L(\vec{c}- \vec{b})}{L+1}$
$\displaystyle \Rightarrow \vec{AM} = \vec{AB}+\vec{BM}=\vec{b} +\frac{L(\vec{c}- \vec{b})}{L+1}$
$\displaystyle = \frac{\vec{b} +L\vec c}{L+1}$
Grandad