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.

- anonymous

- chestercat

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- anonymous

|dw:1327371116945:dw|

- anonymous

How to solve this problem ?
Guys
Thanks

- anonymous

is your question this

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## More answers

- amistre64

|dw:1327371324663:dw|

- amistre64

im assuming v is up too

- amistre64

|dw:1327371386093:dw|

- amistre64

law of cosines ar any rate

- amistre64

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

- anonymous

|dw:1327371436761:dw|

- amistre64

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

- anonymous

How ?

- amistre64

|dw:1327371556791:dw|

- amistre64

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

- amistre64

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

- amistre64

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

- amistre64

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

- anonymous

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

- amistre64

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

- amistre64

the wolf say that gives us 12.9

- amistre64

5.66 if v is pointing up

- anonymous

there is no rule in the question :(

- amistre64

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

- amistre64

|dw:1327371929000:dw|

- anonymous

if it's up

- anonymous

|dw:1327382757289:dw|

- amistre64

vectors are defined by length and direction

- anonymous

How did you get 5.66?

- amistre64

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

- amistre64

law of cosines; thats been posted

- amistre64

i cant recall the dot version of it tho

- anonymous

can you do the step of it please ?

- anonymous

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

- amistre64

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

- amistre64

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

- amistre64

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

- anonymous

i got 32 :(

- anonymous

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

- 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

http://www.wolframalpha.com/input/?i=sqrt%288%5E2+%2B+6%5E2+-2.8.6+cos%2845%29%29

- amistre64

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

- anonymous

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

- amistre64

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

- 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

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

so we didn't use cosine in this problem

- amistre64

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

- amistre64

there more than one way to skin this problem

- anonymous

but we have 8 in U not 4

- amistre64

|dw:1327372925034:dw|

- amistre64

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

- anonymous

is V up or down in your question

- amistre64

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

- anonymous

that1s make sense

- amistre64

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

- anonymous

Thank you Amister64

- amistre64

youre welcome, it was worth the practice :)

- anonymous

|dw:1327384535229:dw|

- anonymous

Thank You Cinar :)

- anonymous

yw

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