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

1. freckles

have you tried using the formula for finding the angle between two vectors?

2. freckles

solve for theta $\cos(\theta)=\frac{ u \cdot v}{|u||v|}$

3. anonymous

cos(theta) = 6 * 7 / |-1| |-4| ?

4. freckles

how did you get that?

5. 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..

6. 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: $<x_1,x_2> \cdot <y_1,y_2>=x_1 y_1 +x_2 y_2$ to find the magnitude, square each component then add those results and take the square root of that sum example: $|<x_1,x_2>|=\sqrt{x^2_1+x^2_2}$

7. anonymous

dot product: 42 + 4 = 46 magnitude: 36 + 1 = 37 = 6.08 ?

8. 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

9. freckles

you still need to find |v|

10. anonymous

i took the square root of 36 + 1 and got 6.08 do i find |v| then same way?

11. freckles

well 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...

12. anonymous

49 + 16 = 65 square root = 8.06

13. freckles

sqrt(49+16)=sqrt(65) then this will be correct

14. freckles

$u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}$

15. freckles

enter this into the formula I gave above and solve for theta

16. 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? <x1,y1> ?

17. 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

18. freckles

I even summarized these values above

19. freckles

$u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}$ $\cos(\theta)=\frac{ u \cdot v}{|u||v|}$ $\cos(\theta)=\frac{46}{\sqrt{37} \sqrt{65}}$

20. anonymous

cos(theta) = 46 / √37 √65

21. anonymous

oh, okay.. i see

22. freckles

last step solve for theta theta is the angle after all

23. anonymous

i got 60.96..

24. 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

25. anonymous

i see, so it would be 20.3 degrees

26. freckles

yes but you need to figure out what you are doing in your calculator so you can get that answer by yourself

27. anonymous

yeah i know, i found out what i did wrong.

28. freckles

well that's great

29. anonymous

thank you so much for your help! you are awesome!

30. freckles

it was no problem