nthenic_oftime
  • nthenic_oftime
please help.. idk how to even figure this out so steps would be nice too. Find the specified vector or scalar. u = -4i + 1j and v = 4i + 1j; Find . ||u+v|| A. Sqrt34 B. 8 C. 5 D. 2
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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phi
  • phi
first add the "corresponding" terms then find the length of the resulting vector (length is sqrt(sum of square of each term))
phi
  • phi
for example the length of 3i+4j is \[ \sqrt{3^2+4^2} = \sqrt{9+16}= \sqrt{25} = 5\]
nthenic_oftime
  • nthenic_oftime
hey thank you for that a answer can you show me how you got got the length of the vector

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phi
  • phi
what did you get for u+v?
nthenic_oftime
  • nthenic_oftime
wait i misunderstood i thought that was the same thing. im so confused
nthenic_oftime
  • nthenic_oftime
first add corresponding terms gives us... i+2j ?
nthenic_oftime
  • nthenic_oftime
idk how to find the length of a vector
phi
  • phi
-4i + 1j 4i + 1j
phi
  • phi
-4i + 4i is not i
nthenic_oftime
  • nthenic_oftime
its 0?
nthenic_oftime
  • nthenic_oftime
i dont understand the whole vector and scalar thing
phi
  • phi
yes, the i's "go away" you are left with 2j
nthenic_oftime
  • nthenic_oftime
which is positive points?
phi
  • phi
in 2-dimensions, you can think of the vector as pair of numbers for example, u= -4i + 1j (which can also be written <-4,1> in a graph, it looks like this: |dw:1443634973472:dw|
phi
  • phi
and the length of the vector is the length of the line from (0,0) (the origin) to the point (-4,1) we use pythagoras to find its length
nthenic_oftime
  • nthenic_oftime
okay so U is a vector and length would be to the point.
nthenic_oftime
  • nthenic_oftime
oh okay i didnt see your message
phi
  • phi
u+v = 2j (or 0i+2j, or (0,2) ) in a graph it looks like this |dw:1443635111360:dw|
nthenic_oftime
  • nthenic_oftime
|dw:1443635167339:dw|
phi
  • phi
we could use pythagoras \[ \sqrt{0^2+2^2}= \sqrt{0+4}= \sqrt{4}= 2 \] but we can see the length is just 2
nthenic_oftime
  • nthenic_oftime
oh cool good so our drawings of vthis match okay so 0^2 because we have no i left and 2^2 becayse 2j
nthenic_oftime
  • nthenic_oftime
i understand thank you so much... can i ask what do i and j standfor why not use x and y? i got behind and i am trying to catch up on things as its obvious i am missing a gfew things in my knowledge
phi
  • phi
The interesting thing is this same idea works for 3-D or even higher dimensions (though visualizing a vector with more than 3 components is beyond me)
phi
  • phi
I'm not sure why people use i,j,k but it does not matter the idea is they are different "dimensions" for example, sideways and up/down. The other way people write vectors is as a "tuple" such as (1,2) or <1,2> where it is understood each number is the distance along each dimension
nthenic_oftime
  • nthenic_oftime
okay so vectors would be written as plot points or coordinates just signified as different dimensions thanks for the help on the problem and that little info there it caught me up a lil bit. medal and fan for you :)

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