Question

What is the angle between vectors $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$with magnitudes 2 and $\sqrt{3}$ respectively? Given $\overrightarrow{a}.\overrightarrow{b}=\sqrt{3}.$

Answer 1

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