Question

Write the angle between two vectors $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$with magnitudes $\sqrt{3}$ and 2 respectively if $\overrightarrow{a}·\overrightarrow{b}=\sqrt{6}.$

Answer 1

$$\begin{gathered} \text{Let θ be the angle between}\overrightarrow{a}\text{and}\overrightarrow{b}\text{.} \\ \text{Given,} \\ \left|\overrightarrow{a}\right|=\sqrt{3};\left|\overrightarrow{b}\right|=2;\overrightarrow{a}.\overrightarrow{b}=\sqrt{6} \\ \text{We know that} \\ \overrightarrow{a}.\overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta \\ \Rightarrow \sqrt{6}=\left(\sqrt{3}\right)\left(2\right)\cos \theta \\ \Rightarrow \cos \theta =\frac{\sqrt{6}}{2\sqrt{3}}=\frac{1}{\sqrt{2}} \\ \Rightarrow \theta ={\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\mathrm{\pi }}{4} \end{gathered}$$