Question

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Answer 1

   
[tex]\displaystyle\\ \text{\bf Se da: } \\\\ \text{Vectorii }~\overrightarrow{u};~\overrightarrow{v} \\\\ \overrightarrow{u}\cdot \overrightarrow{v} =7\\\\ \Big|\overrightarrow{u}\Big|=3\\\\ \Big|\overrightarrow{v}\Big|=4\\\\ \text{\bf Se cere:}\\\\ \cos(\sphericalangle(\overrightarrow{u};~\overrightarrow{v}) ) [/tex]


[tex]\displaystyle\\ \text{\bf Rezolvare:} \\\\ \text{Folosim formula: }~ \overrightarrow{u}\cdot \overrightarrow{v} = \Big|\overrightarrow{u}\Big|\cdot \Big|\overrightarrow{v}\Big|\cdot \cos(\sphericalangle(\overrightarrow{u};~\overrightarrow{v}) ) \\\\\\ 7=3\cdot 4 \cdot \cos(\sphericalangle(\overrightarrow{u};~\overrightarrow{v}) )\\\\ \cos(\sphericalangle(\overrightarrow{u};~\overrightarrow{v}) )= \frac{7}{3\cdot 4}= \boxed{\bf \frac{7}{12}} [/tex]