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

Given

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

Since

`\begin{gathered} \cos\theta=(u\cdot v)/(|u||v|) \\ \\ u\cdot v=(3*7)+(-6*9)=21-54=-33 \\ \\ |u|=√(3^2+(-6)^2)=3√(5) \\ \\ |v|=√(7^2+9^2)=√(130) \\ \end{gathered}`
`\begin{gathered} \Rightarrow\theta=\cos^(-1)(-(33)/(3√(5)*√(130))) \\ \\ \\ \\ \Rightarrow\theta=115.56 \end{gathered}`