Question

Se considera triunghiul ABC , cu AB = 4 , BC = 5 si B = π / 3 . Calculati vectorul BA · vectorul BC.


Daca se poate sa imi spui si formula pe care ai aplicat-o ar fi perfect ,multumesc anticipat !

Answer 1

Se aplica produsul scalar al vectorilor:
vectorul BA*vectorul BC=modulul vectorului BA*modulul vectoruluiBC*cos($\pi /3$)=4*5*cos(60)=20/2=10

Answer 2

$AB = 4\\ BC = 5\\ \\ B = (\widehat{\overrightarrow{BA}, \overrightarrow{BC}}) = \dfrac{\pi}{3}\\ \\ \cos(\widehat{\overrightarrow{BA}, \overrightarrow{BC}}) = \dfrac{\overrightarrow{BA}\cdot\overrightarrow{BC}}{|\overrightarrow{BA}|\cdot |\overrightarrow{BC}|} \\ \\ \\ \cos\dfrac{\pi}{3} = \dfrac{\overrightarrow{BA}\cdot\overrightarrow{BC}}{4\cdot 5}$

$\dfrac{1}{2}= \dfrac{\overrightarrow{BA}\cdot\overrightarrow{BC}}{20}\\ \\\overrightarrow{BA}\cdot \overrightarrow{BC} = \dfrac{1}{2}\cdot 20\\ \\ \Rightarrow \boxed{\overrightarrow{BA}\cdot \overrightarrow{BC} = 10}$