anonymous
  • anonymous
Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, -4>, v = <-4, -3>
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Hi! I can help you! :)
anonymous
  • anonymous
Do you have any ideas about how to get started, or are you completely stuck? :)
johnweldon1993
  • johnweldon1993
Hint...dot product \[\large \vec{u} \cdot \vec{v} = ||u|||v|| \cos(\theta)\] So \[\large cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{||u|| ||v||}\]

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More answers

anonymous
  • anonymous
@BasketWeave completely stuck :-(
anonymous
  • anonymous
Okay, no problem! John's given you a clue here: we can use the dot product.
anonymous
  • anonymous
Do you know how to find the dot product between two vectors? :)
anonymous
  • anonymous
u * v = <-5,-4> , <-4,-3> =-5(-4) + -4(-3) = 20 + 12 = 32 |u| = √(-5)^2 + (-4)^2 =√25 +16 = √41
anonymous
  • anonymous
|v| = √(-4)^2 + (-3)^2 = √16 + 9 = √25 = 5
anonymous
  • anonymous
u * v = 32 |u| =√41 |v| = 5
anonymous
  • anonymous
\[\frac{ 32 }{ \sqrt{41}5} \]
anonymous
  • anonymous
Well done :) Carry on...
anonymous
  • anonymous
im getting 0.02648....
anonymous
  • anonymous
i calculated wrong
anonymous
  • anonymous
now i got, 0.99951.. one of my answer choices is 0.9 degrees, is that correct?
anonymous
  • anonymous
Well, try and remember what that 0.99951 means... :) It's not actually the angle!
johnweldon1993
  • johnweldon1993
Right, that leaves us with \[\large cos(\theta) = 0.99951\] What do you get when you actually solve for the angle?
anonymous
  • anonymous
1.8 degrees?
anonymous
  • anonymous
Excellent, well done!
johnweldon1993
  • johnweldon1993
Correct indeed
anonymous
  • anonymous
thank you guys so much for your help!
anonymous
  • anonymous
You're most welcome :)

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