anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1327371116945:dw|
anonymous
  • anonymous
How to solve this problem ? Guys Thanks
anonymous
  • anonymous
is your question this

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amistre64
  • amistre64
|dw:1327371324663:dw|
amistre64
  • amistre64
im assuming v is up too
amistre64
  • amistre64
|dw:1327371386093:dw|
amistre64
  • amistre64
law of cosines ar any rate
amistre64
  • amistre64
c^2 = 8^2 + 6^2 -2.8.6 cos(45)
anonymous
  • anonymous
|dw:1327371436761:dw|
amistre64
  • amistre64
then change it to the up direction and we get 45+90 as the angle istead of 45
anonymous
  • anonymous
How ?
amistre64
  • amistre64
|dw:1327371556791:dw|
amistre64
  • amistre64
if we know 2 sides and the angles between them the law of cosines from trig gives us the third side
amistre64
  • amistre64
45+90 = 135 so that just the only thing that chagnes from before
amistre64
  • amistre64
c^2 = 8^2 + 6^2 -2.8.6 cos(135)
amistre64
  • amistre64
-v is just the opposite direction; and -2 is stretched twice as far; 3+3 = 6
anonymous
  • anonymous
in the book is given only the answer and the answer is that in the book I U - 2V I = 5.7
amistre64
  • amistre64
that may be; what does the law of C give us?
amistre64
  • amistre64
the wolf say that gives us 12.9
amistre64
  • amistre64
5.66 if v is pointing up
anonymous
  • anonymous
there is no rule in the question :(
amistre64
  • amistre64
so either you meant the v is pointing up; and we get 5.66 or the book is wrong
amistre64
  • amistre64
|dw:1327371929000:dw|
anonymous
  • anonymous
if it's up
anonymous
  • anonymous
|dw:1327382757289:dw|
amistre64
  • amistre64
vectors are defined by length and direction
anonymous
  • anonymous
How did you get 5.66?
amistre64
  • amistre64
if v pointed up then -2v points down and we get u-2v = 5.7
amistre64
  • amistre64
law of cosines; thats been posted
amistre64
  • amistre64
i cant recall the dot version of it tho
anonymous
  • anonymous
can you do the step of it please ?
anonymous
  • anonymous
R^2=6^2+8^2-2*6*8*cos135 R=12.95
amistre64
  • amistre64
we know 2 sides, u and 2v u = 8, 2v = 6 |u-2v|^2 = u^2 + v^2 -2uv cos(t)
amistre64
  • amistre64
since t = 45 as we originally thought; just plug it in :) and we get 5.66
amistre64
  • amistre64
i missed a few typos in there but hopefully you get the picture :)
anonymous
  • anonymous
i got 32 :(
anonymous
  • anonymous
i followed your steps but I didn't get the same answer
amistre64
  • 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
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=sqrt%288%5E2+%2B+6%5E2+-2.8.6+cos%2845%29%29
amistre64
  • amistre64
my us off; forgot how to get a 45 :)
anonymous
  • anonymous
Oh i see now Thank you so much that was very helpful :)
amistre64
  • amistre64
sqrt(2) = 8 1 = c c = 4sqrt(2) thas prolly better
amistre64
  • 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)
amistre64
  • 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 :)
anonymous
  • anonymous
so we didn't use cosine in this problem
amistre64
  • amistre64
we didnt have to, but it was the first idea i had until this one popped up
amistre64
  • amistre64
there more than one way to skin this problem
anonymous
  • anonymous
but we have 8 in U not 4
amistre64
  • amistre64
|dw:1327372925034:dw|
amistre64
  • amistre64
the length of the vector and its angle lets me know how to construct its component parts when I do it right
anonymous
  • anonymous
is V up or down in your question
amistre64
  • amistre64
the answer key would suggest its up to begin with otherwise we cant get the 5.7
anonymous
  • anonymous
that1s make sense
amistre64
  • amistre64
we still had to use some trig, or maybe this is geometry to get the results we wanted tho.
anonymous
  • anonymous
Thank you Amister64
amistre64
  • amistre64
youre welcome, it was worth the practice :)
anonymous
  • anonymous
|dw:1327384535229:dw|
anonymous
  • anonymous
Thank You Cinar :)
anonymous
  • anonymous
yw

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