anonymous
  • anonymous
vectors
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
find two vectors such that mag(u+v)=mag(u) + mag(v) find two vectors such that mag(u-v)=mag(u) - mag(v)
anonymous
  • anonymous
if you make u+v the reflection of u about an axis then you'll have the sum part taken care of.
anonymous
  • anonymous
can you please provide me an example

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anonymous
  • anonymous
oops, i spoke to soon... just a sec.
anonymous
  • anonymous
this has to do with the triangle inequality... ||a||+||b||>=||a+b|| so equality is only with 0 vector or if a & b point in the same direction.
anonymous
  • anonymous
oh makes sense plz go ahead
anonymous
  • anonymous
oops, goofed again as the inequality should be the other way round, i.e., ||a+b||<=||a||+||b|| sorry.
anonymous
  • anonymous
can you provide me an example of u and v where this actually happens
anonymous
  • anonymous
sure... u = <1, 0>, v = <1, 0>, u+v = <2, 0>
anonymous
  • anonymous
arent u and v same vectors
anonymous
  • anonymous
same work for the other one you're looking for. u - v = <0, 0> and ||u|| - ||v|| = 0
anonymous
  • anonymous
yep
anonymous
  • anonymous
but the question is asking for 2 different vectors and the mag (u+v) =2 and mag(u) + mag(v) =4 in your example is not true
anonymous
  • anonymous
if they can't be the same then let u = <1, 0>, v = <2, 0> and u+v = <3, 0> but equality of magnitudes still holds
anonymous
  • anonymous
wrong. ||u|| = ||v|| = 1, ||u+v||= 2
anonymous
  • anonymous
iin example where u = v.
anonymous
  • anonymous
oh ya my bad mag (u+v) =4 and mag(u) + mag(v) =2 still doesnt equals
anonymous
  • anonymous
mag(u+v) = 2 sqrt(2^2 + 0^2) = sqrt(4) = 2
anonymous
  • anonymous
oops sorry :(
anonymous
  • anonymous
it's okay. it's late and i'm tired enough for both of us
anonymous
  • anonymous
hey just a sec the second ex you provided which has two difeerent vector has different magnitudes and they do not equal 1 + sqrt(2) is not equal to 3
anonymous
  • anonymous
never mind i got your point can you plz show me ex of u-v sorry again
anonymous
  • anonymous
only way it happens for that one is the same way... u & v must point in the same direction.
anonymous
  • anonymous
however, ||u|| >=||v|| because ||u-v||>=0
anonymous
  • anonymous
alright so u = 1,0 and v = -2,0 so u+v = -1,0 oh this dooesn't work
anonymous
  • anonymous
wait no it does i guess u + v = 3,0 am i right
anonymous
  • anonymous
they point in opposite directions
anonymous
  • anonymous
so what example do you think would do u-v property true
anonymous
  • anonymous
similar example... u = <2, 0>, v = <1, 0> u-v = <1, 0> ||u|| = 2, ||v|| = 1, ||u-v|| = 1
anonymous
  • anonymous
great thank you
anonymous
  • anonymous
you're welcome

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