Question

Find the angle between two vectors $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$with magnitudes 1 and 2 respectively and when $\left|\overrightarrow{a}\times \overrightarrow{b}\right|=\sqrt{3}.$

Answer 1

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