# I General equation for the magnitude of the difference vector

#### jonander

Summary
General equation for the magnitude of the difference vector of two parallel or antiparallel vectors
Hi everyone,

While finding the solution for one of my exercises, I found the following answer. I'm seriously questioning if the equations provided in that answer are reversed. According to my understanding, if two vectors $\vec{S}$ and $\vec{T}$ are parallel (same direction) the magnitude of the difference vector $\vec{S}-\vec{T}$ is:

$$||\vec{S}| - |\vec{T}||$$

If the vectors are antiparallel, the magnitude of the difference vector is:
$$|\vec{S}| + |\vec{T}|$$

Did the author of that answer wrote the equations in the wrong places or am I missing something?

Thanks.

#### phinds

Gold Member
Sure looks to me like you have it right and he has it reversed from what it should be.

#### jonander

Thanks for the confirmation, phinds.

#### Stephen Tashi

If the vectors are antiparallel, the magnitude of the difference vector is:
$$|\vec{S}| + |\vec{T}|$$
For example, in 2D, let $\vec{S} = \overrightarrow{(1,0)}$ and let $\vec{T} = (-1)(\vec{S}) = \overrightarrow{(-1,0)}$

$\overrightarrow{S-T} = \overrightarrow{(1,0)} - \overrightarrow{(-1,0)} = \overrightarrow{ (2,0)}$.

#### PeroK

Homework Helper
Gold Member
2018 Award
Summary: General equation for the magnitude of the difference vector of two parallel or antiparallel vectors

Hi everyone,

While finding the solution for one of my exercises, I found the following answer. I'm seriously questioning if the equations provided in that answer are reversed. According to my understanding, if two vectors $\vec{S}$ and $\vec{T}$ are parallel (same direction) the magnitude of the difference vector $\vec{S}-\vec{T}$ is:

$$||\vec{S}| - |\vec{T}||$$

If the vectors are antiparallel, the magnitude of the difference vector is:
$$|\vec{S}| + |\vec{T}|$$

Did the author of that answer wrote the equations in the wrong places or am I missing something?

Thanks.
You could try an example where $\vec{T} = \vec{S}$ (parallel) and $\vec{T} = - \vec{S}$ (anti-parallel).

#### jonander

Hi Perok, thanks for replying.

I tried already with a few cases and I'm kind of sure that the author got the equations reversed. I'm asking mostly for confirmation.

#### PeroK

Homework Helper
Gold Member
2018 Award
Hi Perok, thanks for replying.

I tried already with a few cases and I'm kind of sure that the author got the equations reversed. I'm asking mostly for confirmation.
When you say "author", it would help if you said who you were talking about. The page you linked to seemed to be saying what you are saying.

#### Stephen Tashi

I tried already with a few cases and I'm kind of sure that the author got the equations reversed.
You're doing something wrong.

#### PeroK

Homework Helper
Gold Member
2018 Award
You're doing something wrong.
He's confused you too. I think he's saying that what is in that page and in his post are correct!

#### PeroK

Homework Helper
Gold Member
2018 Award
if two vectors $\vec{S}$ and $\vec{T}$ are parallel (same direction) the magnitude of the difference vector $\vec{S}-\vec{T}$ is:

$$||\vec{S}| - |\vec{T}||$$

If the vectors are antiparallel, the magnitude of the difference vector is:
$$|\vec{S}| + |\vec{T}|$$
Just to be clear. Are you saying this is right or wrong?

#### jonander

I'm saying that the author of this answer, got the equations in the wrong places. And what I wrote in my post is what it should be.

#### PeroK

Homework Helper
Gold Member
2018 Award
I'm saying that the author of this answer, got the equations in the wrong places. And what I wrote in my post is what it should be.
They look the same to me!

#### jonander

Oh, indeed, they are the same now. It seems that the edition request has been approved.

#### Stephen Tashi

They look the same to me!
Me too. To be specific, the formulae in the original post look the same as the formulae given in answer 1 on the stackexchange page.

Answer 1 on https://physics.stackexchange.com/questions/304634/what-is-the-magnitude-of-the-difference-vector/304644#304644 :

The magnitude of the difference vectors depends on the orientation of S⃗ and T⃗ . If they are parallel then |S⃗ −T⃗ |=||S⃗ |−|T⃗ || and if they are anti-parallel then |S⃗ −T⃗ |=|S⃗ |+|T⃗ |.
Can answers on stackexchange be edited?

Homework Helper
Gold Member
2018 Award

#### jonander

Sorry for the confusion guys. I saw that that answer was wrong, asked here for confirmation on my alternative, and, after that, I edited the answer in Stack Overflow.

And, yes! Thankfully, answers in StackExchange can be improved/edited.

Last edited: