## katherinekc 2 years ago Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 7>, v = <9, 7>

1. ZeHanz

You could use the formula:$\cos \theta=\frac{ \vec u \cdot \vec v}{ |\vec u||\vec v| }$assuming you are familiar with the dot product of vectors.

2. Sshmoo

here it is on mathematica.

3. katherinekc

that wouldnt let me open it @Sshmoo

4. katherinekc

im just learning it so im still so comfused

5. Sshmoo

i'll try converting it to a different file, all it is is a graph of the vectors and a dot product. It just looks shinier.

6. katherinekc

ohok

7. Sshmoo

here it is in PDF

8. katherinekc

okk hm so

9. katherinekc

so which of these would the answer be ? -8.3° 1.7° 3.3° 13.3°

10. ZeHanz

If you calculate cos theta, you get: $\cos \theta=\frac{ 8 \cdot 9 + 7 \cdot 7 }{ \sqrt{8^2+7^2}\sqrt{9^2+7^2} }=\frac{ 72+49 }{\sqrt{113}\sqrt{130} }=\frac{ 121 }{ \sqrt{113} \sqrt{130}}\approx 0.99833$Now take the inverse cosine (cos^-1 on your calculator) to see the answer.

11. katherinekc

THANK YOU!

12. ZeHanz

yw!