# Find scalar product of leg and side of right triangle

From the figure below

It is given that length of $BC=3# we are asked to find scalar product of vectors$AB$and$BC$I don't know methods to solve such problems and please help me. - I can't parse this. Where's your origin located? – J. M. Aug 16 '11 at 14:11 aa ok see this it is written in georgian language but question is the same as i wrote see it naec.ge/images/doc/MASC_SERT/2011pedagogebi-matematikai.pdf number 19 – dato datuashvili Aug 16 '11 at 14:18 ## 1 Answer If by scalar product, you mean dot product, then the answer would be$-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\$.

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how this equality does hold?BA*BC=|BC||AB|cos(∠ABC) – dato datuashvili Aug 16 '11 at 14:40
sorry i understood – dato datuashvili Aug 16 '11 at 14:41
thanks very much @robjohn i have seen everything and got right answer you answer helped very much thanks ones again – dato datuashvili Aug 16 '11 at 14:49