Find the angle between u =(8,-2) and v =(9,3) round to the nearest tenth of a degree. a.32,5b.6.3c.42.5d.16.3

Find magnitude of each vector.

||u|| = sqrt{8^2 + (-2)^2}

||u|| = sqrt{64 + 4}

||u|| = sqrt{68}

Now the other vector.

||v|| = sqrt{9^2 + 3^3}

||v|| = sqrt{81 + 9}

||v|| = sqrt{90}

Now find u • v.

u•v = <8, -2> <9, 3>

u•v = 8(9) + (-2)(3)

u•v = 72 - 6

u•v = 66

Now use

cos x = (u•v)/||u||•||v||

Remaining Steps:

1. Let u•v = 66

2. Let ||u||•||v|| = sqrt{68}•sqrt{90}

3. Simplify your substitution.

4. Take the arccos on both sides to find x.

Note: x = angle between vectors u and v.

Take it from here.

the angle between u=(8, -2) and v=(9,3) is 32.5°