1. cho \(\left|\overrightarrow{a}\right|=7;\left|\overrightarrow{b}\right|=5\sqrt{2};\overrightarrow{a}.\overrightarrow{b}=\dfrac{35\sqrt{2}}{2}\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
2. cho \(\left|\overrightarrow{a}\right|=4;\left|\overrightarrow{b}\right|=\dfrac{10\sqrt{3}}{3};\overrightarrow{a}.\overrightarrow{b}=\dfrac{20\sqrt{3}}{3}\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
1: \(\overrightarrow{a}\cdot\overrightarrow{b}=\dfrac{35\sqrt{2}}{2}\)
=>\(\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{35\sqrt{2}}{2}\)
=>\(7\cdot5\sqrt{2}\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{35\sqrt{2}}{2}\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{1}{2}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=60^0\)
2: \(\overrightarrow{a}\cdot\overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)\cdot4\cdot\dfrac{10\sqrt{3}}{3}=\dfrac{20\sqrt{3}}{3}\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{1}{2}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)=60^0\)
