# Homework Help: Adding & Subtracting vectors

1. Oct 27, 2012

### Ammar w

1. The problem statement, all variables and given/known data
If two collinear vectors $\vec{A}$ and $\vec{B}$ are added, the resultant has a magnitude equal to 4.0. If $\vec{B}$ is subtracted from $\vec{A}$, the resultant has a magnitude equal to 8.0. What is the magnitude of $\vec{B}$ ?

2. Relevant equations

None.

3. The attempt at a solution

|A| + |B| = 4.0 (1)
|A| - |B| = 8.0 (2)
sum the two equations :
2|A| = 12
=> |A| = 6.0
substitute in (1) :
6.0 + |B| = 4.0
=> |B| = -2

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is this a complete and right solution??
should I draw the vectors??
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 27, 2012

### haruspex

Clearly that's wrong since |B| cannot be negative.
Let's step back a bit. They're added as vectors:
|A+B| = 4
|A-B| = 8
Since they're collinear, you have equated |A+B| to |A|+|B| etc., but there is another possibility. Can you see what it is?

3. Oct 27, 2012

### Ammar w

Thanks haruspex

so the solution :

|A+B| = 4
|A-B| = 8
because they're collinear :
|A| + |B| = 4
|A| - |B| = 8
sum the two equations :
2|A| = 12
|A| = 6
substitute :
6 + |B| = 4
=> |B| = ???

do you mean by drawing??

4. Oct 28, 2012

### haruspex

No, you're still making an assumption that's wrong. What if A and B are in opposite directions?