# Homework Help: Subtracting two vectors

1. Jan 28, 2010

### jwxie

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

1. The problem statement, all variables and given/known data
Please look at the figure on the right hand side

2. Relevant equations
R = A+B
R = A - B

3. The attempt at a solution

So I tried to understand the concept of subtracting vectors.

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)

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

2. Jan 28, 2010

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

3. Jan 28, 2010

### 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

4. Jan 28, 2010

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.

5. Jan 28, 2010

### jwxie

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.

6. Jan 28, 2010

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

7. Jan 28, 2010

### jwxie

Oh Sorry. I meant C, the resultant.

8. Jan 28, 2010

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?

9. Jan 28, 2010

### jwxie

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?

10. Jan 28, 2010

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

11. Jan 28, 2010

### jwxie

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?

12. Jan 28, 2010

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.

13. Jan 28, 2010

### jwxie

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.

14. Jan 28, 2010