1. cho \(\left|\overrightarrow{a}\right|=\sqrt{10};\left|\overrightarrow{b}\right|=\sqrt{7};\overrightarrow{a}.\overrightarrow{b}=\dfrac{\sqrt{5}}{10}\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
2. cho \(\left|\overrightarrow{a}\right|=1;\left|\overrightarrow{b}\right|=5;\overrightarrow{a}.\overrightarrow{b}=\dfrac{\sqrt{3}}{12}\). Tính \(\left(\overrightarrow{a};\overrightarrow{b}\right)\)
1: \(\overrightarrow{a}\cdot\overrightarrow{b}=\dfrac{\sqrt{5}}{10}\)
=>\(\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\sqrt{5}}{10}\)
=>\(\sqrt{10}\cdot\sqrt{7}\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\sqrt{5}}{10}\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\sqrt{5}}{10}:\sqrt{70}=\dfrac{1}{10\sqrt{14}}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)\simeq88^028'\)
2: \(\overrightarrow{a}\cdot\overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cdot cos\left(\overrightarrow{a};\overrightarrow{b}\right)\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)\cdot1\cdot5=\dfrac{\sqrt{3}}{12}\)
=>\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\sqrt{3}}{12}:5=\dfrac{\sqrt{3}}{60}\)
=>\(\left(\overrightarrow{a};\overrightarrow{b}\right)\simeq88^020'\)
