What is the Magnitude of Vector B When Adding and Subtracting Collinear Vectors?

[Ammar w]

Homework Statement

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} ?

Homework Equations

None.

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

====================
is this a complete and right solution??
should I draw the vectors??

 

[haruspex]

Clearly that's wrong since |B| cannot be negative.

|A| + |B| = 4.0 (1)
|A| - |B| = 8.0 (2)

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?

 

[Ammar w]

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.,

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| = ?

but there is another possibility. Can you see what it is?

do you mean by drawing??

 

[haruspex]

|A+B| = 4
|A-B| = 8
because they're collinear :
|A| + |B| = 4
|A| - |B| = 8

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