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

Solution:

Given the vectors;

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

The angle between the two vectors is;

$\theta=\cos^{-1}(\frac{u\cdot v}{|u||v|})$

Where;

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

Also;

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

Thus;

$\begin{gathered} \theta=\cos^{-1}(-\frac{33}{15\sqrt{26}}) \\ \\ \theta=115.56^o \end{gathered}$