# find scalar product of leg and side of right triangle

from the figure below

there is given that length of BC=3 we are asked to find scalar product of vectors AB and BC i dont know methods to solve such problems and please help me

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I can't parse this. Where's your origin located? –  Ｊ. Ｍ. Aug 16 '11 at 14:11
aa ok see this it is written in georgian language but question is the same as i wrote see it naec.ge/images/doc/MASC_SERT/2011pedagogebi-matematikai.pdf number 19 –  dato datuashvili Aug 16 '11 at 14:18

If by scalar product, you mean dot product, then the answer would be $-9$. The definition of cosine says $|\vec{BC}|=|\vec{AB}|\cos(\angle ABC)$; note that $cos(\angle ABC)>0$ since it is acute. Since $\vec{BA}\cdot\vec{BC}=|\vec{BC}||\vec{AB}|\cos(\angle ABC)$ and $\vec{AB}=-\vec{BA}$, we get that $\vec{BA}\cdot\vec{BC}=-|\vec{BC}|^2$.