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anonymous
 one year ago
Find the angle between the given vectors to the nearest tenth of a degree.
u = <6, 1>, v = <7, 4>
anonymous
 one year ago
Find the angle between the given vectors to the nearest tenth of a degree. u = <6, 1>, v = <7, 4>

This Question is Closed

freckles
 one year ago
Best ResponseYou've already chosen the best response.2have you tried using the formula for finding the angle between two vectors?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2solve for theta \[\cos(\theta)=\frac{ u \cdot v}{uv}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cos(theta) = 6 * 7 / 1 4 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2how did you get that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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
 one year ago
Best ResponseYou've already chosen the best response.2it 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: \[<x_1,x_2> \cdot <y_1,y_2>=x_1 y_1 +x_2 y_2\] to find the magnitude, square each component then add those results and take the square root of that sum example: \[<x_1,x_2>=\sqrt{x^2_1+x^2_2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dot product: 42 + 4 = 46 magnitude: 36 + 1 = 37 = 6.08 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[u \cdot v=<6,1> \cdot <7,4>=6(7)+(1)(4)=42+4=46 \\ u=\sqrt{6^2+(1)^2}=\sqrt{36+1}=\sqrt{37}\] almost you forgot to take the square root

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you still need to find v

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i took the square root of 36 + 1 and got 6.08 do i find v then same way?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well if you mean by what I told you above yes \[<x_1,x_2>=\sqrt{x_1^2+x^2_2}\] this is not going to change because you have different numbers in your vector...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.049 + 16 = 65 square root = 8.06

freckles
 one year ago
Best ResponseYou've already chosen the best response.2sqrt(49+16)=sqrt(65) then this will be correct

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[u \cdot v=46 \\ u=\sqrt{37} \\ v=\sqrt{65}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2enter this into the formula I gave above and solve for theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, 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? <x1,y1> ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you do realize the formula is: \[\cos(\theta)=\frac{ u \cdot v}{uv}\] we already found u dot v in the numerator and we already found u and v in denominator

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I even summarized these values above

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[u \cdot v=46 \\ u=\sqrt{37} \\ v=\sqrt{65}\] \[\cos(\theta)=\frac{ u \cdot v}{uv}\] \[\cos(\theta)=\frac{46}{\sqrt{37} \sqrt{65}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cos(theta) = 46 / √37 √65

freckles
 one year ago
Best ResponseYou've already chosen the best response.2last step solve for theta theta is the angle after all

freckles
 one year ago
Best ResponseYou've already chosen the best response.2maybe 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
 one year ago
Best ResponseYou've already chosen the best response.0i see, so it would be 20.3 degrees

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yes but you need to figure out what you are doing in your calculator so you can get that answer by yourself

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah i know, i found out what i did wrong.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much for your help! you are awesome!
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