SOLUTION: Find the angle between the vectors U = <-2,-1> and V + <-3,1>

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Question 857574: Find the angle between the vectors U = <-2,-1> and V + <-3,1>
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the dot product,
U%2AV=abs%28U%29abs%28V%29cos%28theta%29
cos%28theta%29=%28U%2AV%29%2F%28abs%28U%29abs%28V%29%29
The dot product is
U%2AV=-2%2A-3%2B-1%2A1=6-1=5
abs%28U%29=sqrt%28%28-2%29%5E2%2B%28-1%29%5E2%29=sqrt%285%29
abs%28V%29=sqrt%28%28-3%29%5E2%2B%281%29%5E2%29=sqrt%2810%29
So then,
cos%28theta%29=%285%29%2Fsqrt%2850%29
cos%28theta%29=sqrt%2825%29%2Fsqrt%2850%29
cos%28theta%29=sqrt%281%2F2%29
cos%28theta%29=sqrt%282%29%2F2
theta=45