Solution
We are required to find the angles between two vectors.
We will use the formula
[tex]q.r=\lvert q\rvert\lvert r\rvert\cos\theta[/tex]where θ is the angle between the vectors
[tex]\begin{gathered} q.r=(2\times-3)+(6\times4) \\ q.r=18 \end{gathered}[/tex][tex]\lvert{q}\rvert=\sqrt{2^2+6^2}=\sqrt{40}=6.3246[/tex][tex]\lvert{r}\rvert=\sqrt{(-3)^2+4^2}=\sqrt{25}=5[/tex]Plug in the values obtained into the formula
[tex]\begin{gathered} 18=6.3246\times5\times\cos\theta \\ \cos\theta=0.5692 \\ \theta=\cos^{-1}(0.5692) \\ \theta=55.3^0 \end{gathered}[/tex]