Question

Find the angle between the vectors for u and v given below.

u=<4,3> v=<-2,4>

Answer 1

\[u \cdot v=||u||*||v||\cos(\theta)\]
So:
\[\arccos(\frac{u \cdot v}{||u||*||v||})=\theta\]
\[u \cdot v=(4)(-2)+(3)(4)=-8+12=4\]
\[||u||=\sqrt{16+9}=5\]
\[||v||=\sqrt{4+16}=\sqrt{20}\]
So:
\[\theta=\arccos(\frac{4}{5\sqrt{20}})=79.7 \]
degrees

Answer 2

Thank you very much. I had it right I was just taking cos not arccos. thank you very much

Answer 3

No problem :P