# General equation for the magnitude of the difference vector

• I
• jonander
In summary, the conversation is about the correct equations for finding the magnitude of the difference vector between two parallel or antiparallel vectors. The original post on StackExchange had incorrect equations, but the author has since edited them. The summary also mentions the confusion and confirmation from other users.
jonander
TL;DR 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.

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.

jonander said:
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)}##.

jonander said:
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).

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.

jonander said:

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.

jonander said:
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.

Stephen Tashi said:
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!

jonander said:
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?

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.

jonander said:
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
PeroK said:
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.

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?

jonander and PeroK
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:

## 1. What is the general equation for the magnitude of the difference vector?

The general equation for the magnitude of the difference vector is given by the Pythagorean theorem, which states that the magnitude of the difference vector is equal to the square root of the sum of the squares of the components of the vector.

## 2. How is the magnitude of the difference vector calculated?

The magnitude of the difference vector is calculated by taking the square root of the sum of the squares of the components of the vector. This can be represented mathematically as: ||a-b|| = √( (ax - bx)2 + (ay - by)2 + (az - bz)2 )

## 3. What does the magnitude of the difference vector represent?

The magnitude of the difference vector represents the distance between two points in space. It is a measure of the length of the vector that connects the two points.

## 4. Can the magnitude of the difference vector be negative?

No, the magnitude of the difference vector is always a positive value. This is because it is calculated using the square root, which always results in a positive number.

## 5. How is the magnitude of the difference vector used in physics?

In physics, the magnitude of the difference vector is often used to calculate the distance between two objects or points in space. It is also used in vector addition and subtraction to determine the resultant vector. Additionally, it is an important concept in understanding the concept of displacement and velocity in kinematics.

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