Question

If $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$are two vectors such that $\left|\overrightarrow{a}\right|=4,\left|\overrightarrow{b}\right|=3\mathrm{and}\overrightarrow{a}·\overrightarrow{b}=6$, find the angle between $\overrightarrow{a}\mathrm{and}\overrightarrow{b}.$

Answer 1

$$\begin{gathered} \text{Let}\theta \text{be the angle between}\overrightarrow{a}\text{and}\overrightarrow{b}. \\ \text{Given that} \\ \overrightarrow{a}.\overrightarrow{b}=6 \\ \Rightarrow \left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta =6 \\ \Rightarrow \left(4\right)\left(3\right)\cos \theta =6 \\ \Rightarrow 12\cos \theta =6 \\ \Rightarrow \cos \theta =\frac{6}{12}=\frac{1}{2} \\ \Rightarrow \theta ={\cos }^{-1}\left(\frac{1}{2}\right)=\frac{\mathrm{\pi }}{3} \end{gathered}$$