SOLUTION: u: <3, -1> v: <4, 3> w: <&#8532; , -8/9 > What's the angle between u and v ? A.) 48.2 B.) 55.3 C.) 58.6 D.) 61.1

Algebra ->  Test -> SOLUTION: u: <3, -1> v: <4, 3> w: <&#8532; , -8/9 > What's the angle between u and v ? A.) 48.2 B.) 55.3 C.) 58.6 D.) 61.1      Log On


   

Question 1070967: u: <3, -1>
v: <4, 3>
w: <⅔ , -8/9 >
What's the angle between u and v ?
A.) 48.2
B.) 55.3
C.) 58.6
D.) 61.1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28abs%28u%29%29=sqrt%283%5E2%2B%28-1%29%5E2%29=sqrt%289%2B1%29=sqrt%2810%29
abs%28%28v%29%29=%284%5E2%2B3%5E2%29=sqrt%2816%2B9%29=sqrt%2825%29=5
If the angle between u and v is theta ,
abs%28abs%28u%29%29%2Aabs%28abs%28v%29%29%2Acos%28theta%29=u%2Av
Substituting,
5sqrt%2810%29%2Acos%28theta%29=3%2A4%2B3%28-1%29
5sqrt%2810%29cos%28theta%29=9
cos%28theta%29=9%2F5sqrt%2810%29=about0.5692
When I calculate that and then apply the inverse cosine function,
I get highlight%28theta=55.3%5Eo%29 .