Understanding Vector Subtraction: A Guide for Solving Vector Problems

[jwxie]

This is not a homework question, just a coursework reading.

Homework Statement

Please look at the figure on the right hand side

Homework Equations

R = A+B
R = A - B

The Attempt at a Solution

So I tried to understand the concept of subtracting vectors.
I want to do the adding convention instead of subtracting them.

If I move A to connect to B (Tip Tail method), then I would have C (resultant) in an opposition direction (now going up from B to A).

So I thought C = B+A, yet since the original problem is opposite direction, I say C = -(B+A)
But that's wrong since C = A - B

For the figure on the left hand. I can do the adding convention.
Reverse the initial B to positive direction (dot line), and so C = A + B.
Therefore, the actual answer is just C = A + (-B)

Please help me to correct my misunderstanding with subtracting vector. I remember back in high school my teacher told me NEVER THINK ABOUT SUBTRACTING, DO ADDING.

The reason I want to understand is that, if the question asks me "bases on the figure on the right hand, find C" I would be wrong

 

[radou]

Why can't you apply the figure (a) to the problem (b)?

 

[jwxie]

Hi,

Even if I move vector B freely to A (tip-tail), and I can't get -B

In figure a I changed B from downward to upward.

Thanks

 

[radou]

If it's easier, first change the direction of vector B (in order to obtain -B), and then move it to A, respecting the rules of vector addition.

 

[jwxie]

If it's easier, first change the direction of vector B (in order to obtain -B), and then move it to A, respecting the rules of vector addition.

But why do we need to change the direction when the question asks find R.
Originally, B and A are in positive direction (up ward). So assuming B and A are free vectors, just as in figure A, I can move any vector til-tail.

Since they are all upward, there is no reason why I need to reverse the direction of B.

I mean let's not say "produce -B". When I see the problem "find R". I did that method and the answer is obvious wrong

C = A - B
4 = 6 - 2 =/ ||| 8 = 6+2 unless you are talking about the difference in units, then subtracting makes sense. But that's very confusing when it comes to a number in calculation unless A - B is stated.

 

[radou]

Wait a minute, what exactly is your "R"?

 

[jwxie]

Wait a minute, what exactly is your "R"?

Oh Sorry. I meant C, the resultant.

 

[radou]

Just to point out, the resultant is the vector which you get when you add a number of vectors. Since, when "subtracting", you only add opposite vectors, the sum is still a resultant. It's just a term for a sum. So, what exactly are you trying to do?

 

[jwxie]

Just to point out, the resultant is the vector which you get when you add a number of vectors. Since, when "subtracting", you only add opposite vectors, the sum is still a resultant. It's just a term for a sum. So, what exactly are you trying to do?

Hi,

Thanks. So if we look at figure b, let's assume it is a question.
Find C.

When I see this problem, I would first do tip-tail method, which is really adding vectors.
So I move B to A.
I find both upward direction, so A + B = C.
Let A = 10, B = 15
C = 25

But now back to the reality. The original C was downward, but in ti-tail, I see C upward. Now I think it's okay since the magnitude is the same.

But why would people do A - B in the first place?

 

[radou]

If A = 10, and B = 15, C does not equal 25. Further on, C = A + B and C' = A - B have different magnitudes.

 

[jwxie]

If A = 10, and B = 15, C does not equal 25. Further on, C = A + B and C' = A - B have different magnitudes.

Oh, I didn't realize C is longer than C'.

IF the question says "Find C with original figure b"
By looking at the picture, just because C is downward, we assume it has to be A - B?

 

[radou]

We see C (in figure (b) ) equals A - B because the laws of vector addition (subtraction). It doesn't matter where it's pointing. You could rotate the whole picture by an amount, but C would still be equal to A - B.

 

[jwxie]

We see C (in figure (b) ) equals A - B because the laws of vector addition (subtraction). It doesn't matter where it's pointing. You could rotate the whole picture by an amount, but C would still be equal to A - B.

the laws of vector addition (subtraction)

A - B = A + (-B)

What I really don't understand is, why would we ever consider subtraction when the problem asks "find C"
A + B = C
Obviously A + B produces a longer C than A - B.
Unless the problem says "A - B = ? " then I know how to do the math 10 - 5 = 5, so C = 5

Where does -B coming from in figure b? Unless this -B comes from the original B in figure a, then it makes sense C is A - B since adding A + - B.

But I am so confused when the figure b is its own original, assuming figure a never exist.

 

[radou]

Unless the problem says "A - B = ? " then I know how to do the math 10 - 5 = 5, so C = 5

Do you understand that this does not hold (unless the vectors are parallel to each other)?

 

[jwxie]

Do you understand that this does not hold (unless the vectors are parallel to each other)?

The numbers are just there for "saying", not for real demonstration.
But again,

when the figure b is its own original, assuming figure a never exist, a - b will not exist, then finding c will just = a + b