Question

The rectangular components of a vector are (2,2). The corresponding rectangular components of another vector are (1,sqrt(3)). Find the angle between the two vectors.

Answer 1

Dear Student,
$$\begin{gathered} letthesearetwovectorsintwodimensionthen \\ A=2i+2j \\ B=i+\sqrt{3}j \\ here\left|A\right|=2\sqrt{2}and\left|B\right|=4 \\ soA.B=\left(2i+2j\right).\left(i+\sqrt{3}j\right)=AB\cos \left(\theta \right) \\ \cos \left(\theta \right)=2+2\sqrt{3}/8\sqrt{2} \\ so\theta ={\cos }^{-1}\left(2+2\sqrt{3}/8\sqrt{2}\right) \end{gathered}$$
Regard