## anonymous 4 years ago I NEED VECTOR HELP!!! CAN ANYONE HERE DO CAL 2 CALCULATIONS???

1. anonymous

Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.

2. anonymous

ANYONE????

3. anonymous

I tried, sitting this one out. Will be watching with great interest.

4. anonymous

ROACHIE sorry :(

5. anonymous

:P

6. anonymous

ill give you a medal if someone figures this out...lol

7. anonymous

ah!

8. anonymous

what is the magnitude of u?

9. anonymous

|v|=10

10. anonymous

6a + 8b = $\left| u \right|$ (10)(1/2)

11. anonymous

... u?

12. anonymous

by theorem 3 we need u * v = $\left| v \right| \left| u \right|$ cos 60

13. anonymous

would u be 1?

14. anonymous

$\sqrt{a ^{2}+b^{2}}$

15. anonymous

if i knew what the magnitude of u was i could figure this problem out.

16. anonymous

oh, u=<6,8>??

17. anonymous

right?

18. anonymous

u = <a,b>

19. anonymous

v = <6,8>

20. anonymous

the magnitude of u (unit vector) is 1 i dont remember the formula for that theorem you were referring

21. anonymous

yea, I dont know where u came from but yes, u being a unit vector has magnitude 1

22. anonymous

6a + 8b = 5 therefore b=5/8 - 3/4a

23. anonymous

a^2 + (5/8 -3/4a)^2 = 1

24. anonymous

?? any thoughts on that?

25. anonymous

where does the 5 come from?

26. anonymous

1/2 (10)

27. anonymous

u * v = |v||u| cos 60 now I see u, duh

28. anonymous

why are we dividing 10 (|v|) by 2

29. anonymous

cos of 60 is 1/2

30. anonymous

someone want to factor that out for me...

31. anonymous

because im sure to f THAT up.

32. anonymous

if we know that u is a unit vector then v * u = |v|cos 60 if you unit vector v then v*u = cos 60 that how I think of it...

33. anonymous

im not following r . . . . .

34. anonymous

haha...25/64 -30/32a +9/16a^2

35. anonymous

v-hat = v/|v|

36. anonymous

then quadratic... fun fun

37. anonymous

|v-hat|=1

38. anonymous

30/32 +- $\sqrt{30/32^{2}-4(25/64)(9/16)}/2(25/64)$

39. anonymous

fml

40. anonymous

did you add the original a^2 to the factor? dumbcow?

41. anonymous

no i didn;t multiply everything by 64 100a^2 -60a -39 = 0 a = -.3928, .9928

42. anonymous

then i need to plug those back into 5/8 -3/4a to find b right?

43. anonymous

yep

44. anonymous

<-.3928,.9196> and <.9928, -.1196>

45. anonymous

looks good

46. anonymous

YES!!!!!

47. anonymous

thank god!