Can some explain vector a+b must be great than a-b

[PoohBah716]

Homework Statement

Can some explain vector a+b must be great than a-b

Homework Equations

none this is conceptual

The Attempt at a Solution

I believe this is false because the direction can be + or -. can you explain to your thoughts

 

[berkeman]

Homework Statement

Can some explain vector a+b must be great than a-b

Homework Equations

none this is conceptual

The Attempt at a Solution

I believe this is false because the direction can be + or -. can you explain to your thoughts

It is certainly not true in general (not even for scalars). You would need to constrain a and b more to have something that was true.

 

[drvrm]

Can some explain vector a+b must be great than a-b

Homework Equations

none this is conceptual

The Attempt at a Solution

I believe this is false because the direction can be + or -. can you explain to your thoughts

i think one should try checking the contention that addition of two vectors must be greater than subtraction - as it is true in case of scalars.

as vectors are having magnitude as well as direction -their addition and subtraction will result into a vector and its magnitude and direction will depend on the angular relation between them -
suppose the angle between them is 180 degree-then their addition will give you a vector which is smaller than the magnitude of a vector when you subtract one from another.

however if the angle between them is zero their addition will give you a vector larger than the result after taking a difference.
you can try taking an arbitrary angle between them and find the conditions for which the 'contention' holds or does not hold.

 

[berkeman]

as it is true in case of scalars.

Is it? Not unless you constrain it to positive scalars...