anonymous
  • anonymous
Find the angle between the given vectors to the nearest tenth of a degree. u = <6, -1>, v = <7, -4>
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
have you tried using the formula for finding the angle between two vectors?
freckles
  • freckles
solve for theta \[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\]
anonymous
  • anonymous
cos(theta) = 6 * 7 / |-1| |-4| ?

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freckles
  • freckles
how did you get that?
anonymous
  • anonymous
i just plug in the numbers from the question to the formula you gave me. im sorry, i really dont know how to do this..
freckles
  • freckles
it doesn't look like you tried to find the dot product of the two vectors nor the magnitude of each vector dot product: you multiply corresponding components and then add those results: example: \[ \cdot =x_1 y_1 +x_2 y_2\] to find the magnitude, square each component then add those results and take the square root of that sum example: \[||=\sqrt{x^2_1+x^2_2}\]
anonymous
  • anonymous
dot product: 42 + 4 = 46 magnitude: 36 + 1 = 37 = 6.08 ?
freckles
  • freckles
\[u \cdot v=<6,-1> \cdot <7,-4>=6(7)+(-1)(-4)=42+4=46 \\ |u|=\sqrt{6^2+(-1)^2}=\sqrt{36+1}=\sqrt{37}\] almost you forgot to take the square root
freckles
  • freckles
you still need to find |v|
anonymous
  • anonymous
i took the square root of 36 + 1 and got 6.08 do i find |v| then same way?
freckles
  • freckles
well if you mean by what I told you above yes \[||=\sqrt{x_1^2+x^2_2}\] this is not going to change because you have different numbers in your vector...
anonymous
  • anonymous
49 + 16 = 65 square root = 8.06
freckles
  • freckles
sqrt(49+16)=sqrt(65) then this will be correct
freckles
  • freckles
\[u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}\]
freckles
  • freckles
enter this into the formula I gave above and solve for theta
anonymous
  • anonymous
okay, so the formula is cos(theta) = u * v / |u| |v| cos(theta) - u * v / |46| |√37| what would be the values of u and v? ?
freckles
  • freckles
you do realize the formula is: \[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\] we already found u dot v in the numerator and we already found ||u| and |v| in denominator
freckles
  • freckles
I even summarized these values above
freckles
  • freckles
\[u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}\] \[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\] \[\cos(\theta)=\frac{46}{\sqrt{37} \sqrt{65}}\]
anonymous
  • anonymous
cos(theta) = 46 / √37 √65
anonymous
  • anonymous
oh, okay.. i see
freckles
  • freckles
last step solve for theta theta is the angle after all
anonymous
  • anonymous
i got 60.96..
freckles
  • freckles
maybe you entered something wrong I'm getting this: http://www.wolframalpha.com/input/?i=arccos%2846%2F%28sqrt%2837%29*sqrt%2865%29%29%29
anonymous
  • anonymous
i see, so it would be 20.3 degrees
freckles
  • freckles
yes but you need to figure out what you are doing in your calculator so you can get that answer by yourself
anonymous
  • anonymous
yeah i know, i found out what i did wrong.
freckles
  • freckles
well that's great
anonymous
  • anonymous
thank you so much for your help! you are awesome!
freckles
  • freckles
it was no problem

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