1. cho \(\left|\overrightarrow{a}\right|=2;\left|\overrightarrow{b}\right|=10;\overrightarrow{a}.\overrightarrow{b}=10\sqrt{3}\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
2. cho \(\left|\overrightarrow{a}\right|=\dfrac{\sqrt{2}}{3};\left|\overrightarrow{b}\right|=9;\overrightarrow{a}.\overrightarrow{b}=3\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
1: \(\overrightarrow{a}\cdot\overrightarrow{b}=10\sqrt{3}\)
=>\(\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=10\sqrt{3}\)
=>\(20\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=10\sqrt{3}\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\sqrt{3}}{2}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=30^0\)
2: \(\overrightarrow{a}\cdot\overrightarrow{b}=3\)
=>\(\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=3\)
=>\(\dfrac{\sqrt{2}}{3}\cdot9\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=3\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{1}{\sqrt{2}}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=45^0\)
