Question

vectors

Answer 1

find two vectors such that mag(u+v)=mag(u) + mag(v)
find two vectors such that mag(u-v)=mag(u) - mag(v)

Answer 2

if you make u+v the reflection of u about an axis then you'll have the sum part taken care of.

Answer 3

can you please provide me an example

Answer 4

oops, i spoke to soon... just a sec.

Answer 5

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.

Answer 6

oh makes sense plz go ahead

Answer 7

oops, goofed again as the inequality should be the other way round, i.e.,
||a+b||<=||a||+||b||

sorry.

Answer 8

can you provide me an example of u and v where this actually happens

Answer 9

sure... u = <1, 0>, v = <1, 0>, u+v = <2, 0>

Answer 10

arent u and v same vectors

Answer 11

same work for the other one you're looking for.
u - v = <0, 0> and ||u|| - ||v|| = 0

Answer 12

yep

Answer 13

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

Answer 14

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

Answer 15

wrong. ||u|| = ||v|| = 1, ||u+v||= 2

Answer 16

iin example where u = v.

Answer 17

oh ya my bad
mag (u+v) =4 and mag(u) + mag(v) =2
still doesnt equals

Answer 18

mag(u+v) = 2 sqrt(2^2 + 0^2) = sqrt(4) = 2

Answer 19

oops sorry :(

Answer 20

it's okay. it's late and i'm tired enough for both of us

Answer 21

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

Answer 22

never mind i got your point can you plz show me ex of u-v sorry again

Answer 23

only way it happens for that one is the same way... u & v must point in the same direction.

Answer 24

however, ||u|| >=||v|| because ||u-v||>=0

Answer 25

alright so u = 1,0 and v = -2,0 so u+v = -1,0 oh this dooesn't work

Answer 26

wait no it does i guess u + v = 3,0 am i right

Answer 27

they point in opposite directions

Answer 28

so what example do you think would do u-v property true

Answer 29

similar example...
u = <2, 0>, v = <1, 0> u-v = <1, 0>
||u|| = 2, ||v|| = 1, ||u-v|| = 1

Answer 30

great thank you

Answer 31

you're welcome