## anonymous 4 years ago The magnitudes of the vectors shown are I U I = 8 and I V I= 3. The vector V is vertical. Graphically determine the magnitude of the vector U - 2V.

1. anonymous

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2. anonymous

How to solve this problem ? Guys Thanks

3. anonymous

is your question this

4. amistre64

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5. amistre64

im assuming v is up too

6. amistre64

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7. amistre64

law of cosines ar any rate

8. amistre64

c^2 = 8^2 + 6^2 -2.8.6 cos(45)

9. anonymous

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10. amistre64

then change it to the up direction and we get 45+90 as the angle istead of 45

11. anonymous

How ?

12. amistre64

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13. amistre64

if we know 2 sides and the angles between them the law of cosines from trig gives us the third side

14. amistre64

45+90 = 135 so that just the only thing that chagnes from before

15. amistre64

c^2 = 8^2 + 6^2 -2.8.6 cos(135)

16. amistre64

-v is just the opposite direction; and -2 is stretched twice as far; 3+3 = 6

17. anonymous

in the book is given only the answer and the answer is that in the book I U - 2V I = 5.7

18. amistre64

that may be; what does the law of C give us?

19. amistre64

the wolf say that gives us 12.9

20. amistre64

5.66 if v is pointing up

21. anonymous

there is no rule in the question :(

22. amistre64

so either you meant the v is pointing up; and we get 5.66 or the book is wrong

23. amistre64

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24. anonymous

if it's up

25. anonymous

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26. amistre64

vectors are defined by length and direction

27. anonymous

How did you get 5.66?

28. amistre64

if v pointed up then -2v points down and we get u-2v = 5.7

29. amistre64

law of cosines; thats been posted

30. amistre64

i cant recall the dot version of it tho

31. anonymous

can you do the step of it please ?

32. anonymous

R^2=6^2+8^2-2*6*8*cos135 R=12.95

33. amistre64

we know 2 sides, u and 2v u = 8, 2v = 6 |u-2v|^2 = u^2 + v^2 -2uv cos(t)

34. amistre64

since t = 45 as we originally thought; just plug it in :) and we get 5.66

35. amistre64

i missed a few typos in there but hopefully you get the picture :)

36. anonymous

i got 32 :(

37. anonymous

i followed your steps but I didn't get the same answer

38. amistre64

or .... u = <8,8> v = <0,3> u = <8,8> -2v = <0,-6> ---------- <8,2> sqrt(8^2+2^2) = sqrt(68) ..... ugh, that aint 5.7 either is it

39. amistre64
40. amistre64

my us off; forgot how to get a 45 :)

41. anonymous

Oh i see now Thank you so much that was very helpful :)

42. amistre64

sqrt(2) = 8 1 = c c = 4sqrt(2) thas prolly better

43. amistre64

u = <4.2,4.2> v = < 0 , 3 > u = <4.2,4.2> -2v = < 0 , -6> ---------- <4.2, 4.2-6> sqrt(32+36+32-24.2) hopefullt i did that right; assume .2 means sqrt(2)

44. amistre64

http://www.wolframalpha.com/input/?i=sqrt%28%284sqrt%282%29%29%5E2%2B%284sqrt%282%29-6%29%5E2%29 yeah, when I actually do it right it works out the same :)

45. anonymous

so we didn't use cosine in this problem

46. amistre64

we didnt have to, but it was the first idea i had until this one popped up

47. amistre64

there more than one way to skin this problem

48. anonymous

but we have 8 in U not 4

49. amistre64

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50. amistre64

the length of the vector and its angle lets me know how to construct its component parts when I do it right

51. anonymous

is V up or down in your question

52. amistre64

the answer key would suggest its up to begin with otherwise we cant get the 5.7

53. anonymous

that1s make sense

54. amistre64

we still had to use some trig, or maybe this is geometry to get the results we wanted tho.

55. anonymous

Thank you Amister64

56. amistre64

youre welcome, it was worth the practice :)

57. anonymous

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58. anonymous

Thank You Cinar :)

59. anonymous

yw