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From the figure below enter image description here

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.

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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 number 19 – dato datuashvili Aug 16 '11 at 14:18
up vote 1 down vote accepted

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

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