Question

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

Answer 1

Given the vectors;

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

The angle between the two vectors is;

`\theta=\cos^(-1)((u\cdot v)/(|u||v|))`

Where;

`\begin{gathered} u\cdot v=(3)(7)+(-6)(9) \\ \\ u\cdot v=21-54 \\ \\ u\cdot v=-33 \end{gathered}`

Also;

`\begin{gathered} |u|=√(3^2+(-6)^2)=√(45) \\ \\ |v|=√(7^2+9^2)=√(130) \\ \\ |u||v|=√(45)*√(130) \\ \\ |u||v|=15√(26) \end{gathered}`

Thus;

`\begin{gathered} \theta=\cos^(-1)(-(33)/(15√(26))) \\ \\ \theta=115.56^o \end{gathered}`