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

• PoohBah716
In summary, the conversation discusses the concept of vector addition and subtraction, and whether the statement "vector a+b must be greater than a-b" is true. The participants come to the conclusion that this is not necessarily true, as the magnitude and direction of the resulting vector depends on the angular relationship between the two vectors. They suggest exploring different angles to determine the conditions under which the statement holds true. Additionally, it is noted that this statement is only true for positive scalars, and not in all cases.

## 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

PoohBah716 said:

## 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.

Chestermiller
PoohBah716 said:
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.

drvrm said:
as it is true in case of scalars.
Is it? Not unless you constrain it to positive scalars...

drvrm