# Finding a vector from the sides of a triangle

• Nov 13th 2009, 09:18 AM
knuckles1234
Finding a vector from the sides of a triangle
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.
• Nov 13th 2009, 12:37 PM
Hello knuckles1234
Quote:

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

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

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