Question

QuestionFind the angle between the given vectors. Round your answer, in degrees, to two decimal places.u = (3, -6), v = (7,9)

Answer 1

Solution

Given

$u=<3,-6>,v=<7,9>$

Since

$\begin{gathered} \cos\theta=\frac{u\cdot v}{|u||v|} \\ \\ u\cdot v=(3\times7)+(-6\times9)=21-54=-33 \\ \\ |u|=\sqrt{3^2+(-6)^2}=3\sqrt{5} \\ \\ |v|=\sqrt{7^2+9^2}=\sqrt{130} \\ \end{gathered}$$\begin{gathered} \Rightarrow\theta=\cos^{-1}(-\frac{33}{3\sqrt{5}\times\sqrt{130}}) \\ \\ \\ \\ \Rightarrow\theta=115.56 \end{gathered}$