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find two vectors such that mag(u+v)=mag(u) + mag(v) find two vectors such that mag(u-v)=mag(u) - mag(v)
if you make u+v the reflection of u about an axis then you'll have the sum part taken care of.
can you please provide me an example
oops, i spoke to soon... just a sec.
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.
oh makes sense plz go ahead
oops, goofed again as the inequality should be the other way round, i.e., ||a+b||<=||a||+||b|| sorry.
can you provide me an example of u and v where this actually happens
sure... u = <1, 0>, v = <1, 0>, u+v = <2, 0>
arent u and v same vectors
same work for the other one you're looking for. u - v = <0, 0> and ||u|| - ||v|| = 0
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
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
wrong. ||u|| = ||v|| = 1, ||u+v||= 2
iin example where u = v.
oh ya my bad mag (u+v) =4 and mag(u) + mag(v) =2 still doesnt equals
mag(u+v) = 2 sqrt(2^2 + 0^2) = sqrt(4) = 2
oops sorry :(
it's okay. it's late and i'm tired enough for both of us
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
never mind i got your point can you plz show me ex of u-v sorry again
only way it happens for that one is the same way... u & v must point in the same direction.
however, ||u|| >=||v|| because ||u-v||>=0
alright so u = 1,0 and v = -2,0 so u+v = -1,0 oh this dooesn't work
wait no it does i guess u + v = 3,0 am i right
they point in opposite directions
so what example do you think would do u-v property true
similar example... u = <2, 0>, v = <1, 0> u-v = <1, 0> ||u|| = 2, ||v|| = 1, ||u-v|| = 1
great thank you