Impossible vector problem. Help

In summary, you are saying that you have the equation x_1+ x_2+ ...+ x_n= F where x_1,... x_{n-1} are the known vector forces, x_n is the one unknown vector and F is the known resultant. Solve that exactly the way you would any equation: x_n= F- x_1- x_2- ...- x_{n-1}. Essentially that "subtraction" on the right is just like addition of vectors except that you reverse the direction of x_1,... x_{n-1}. You might find the calculation easier as -x_n= x_1+ x_2
  • #1
relativitydude
70
0
Most of the time, one uses vectors to find an overall magnitude acting on something, but I need to go in reverse.

Say I know there are a slew of charges and the center one feels a force of some magnitude and there is one undefined vector (magnitude and angle unknown) I would think if you know the overall vector, one could calculate the missing vector in terms of magnitude and angle.

I want to solve for this unknown vector but I have no idea how. It seems impossible.
 
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  • #2
Essentially, you are saying that you have the equation
[tex]x_1+ x_2+ ...+ x_n= F[/tex] where [tex]x_1,... x_{n-1}[/tex] are the known vector forces, [tex]x_n[/tex] is the one unknown vector and F is the known resultant. Solve that exactly the way you would any equation: [tex]x_n= F- x_1- x_2- ...- x_{n-1}[/tex]. Essentially that "subtraction" on the right is just like addition of vectors except that you reverse the direction of [tex]x_1,... x_{n-1}[/tex]. You might find the calculation easier as [tex]-x_n= x_1+ x_2+ ...+ x_{n-1}- F[/tex]. That is, you just reverse the direction of F, add the vectors and then reverse the direction of the result to find [tex]x_n[/tex].
 
  • #3
Consider the vector equation:
[tex]\vec{F}_{net} = \vec{F}_{known} + \vec{F}_{unknown}[/tex]

Where F(net) is the net force at the center and F(known) is the sum of the known forces from each charge. To solve for the unknown vector, F(unknown), just subtract.

(Looks like Halls beat me to it.)
 
  • #4
Overall Magnitude = sqrt( (mag1*cos(A) + mag2*cos(B) + mag3*cos(C))^2 + (mag1*sin(A) + mag2*sin(B) + mag3*sin(C))^2)

I don't think it's that easy since the angle and magnitude go hand in hand. I need to solve for both mag1 and angle A. I'm sorry if I forgot to really point that out.

I thought it would be something more involved along the lines of langrange multipliers.
 
  • #5
relativitydude said:
I don't think it's that easy since the angle and magnitude go hand in hand. I need to solve for both mag1 and angle A. I'm sorry if I forgot to really point that out.
Instead of using overall magnitude, find the vector components. If you write the vectors in terms of their components, adding and subtracting will be a breeze. Once you find the components of the unknown vector, then you can determine its magnitude and angle.

I thought it would be something more involved along the lines of langrange multipliers.
:eek:
 
  • #6
Yes, using the horizontal and vertical components would be really easy but I only know the overall magnitude :(
 
  • #7
If all you know is the magnitude, then you can't solve the problem. I suspect that you know both the magnitude and the angle. Use those to find the components.
 
  • #8
relativitydude said:
Most of the time, one uses vectors to find an overall magnitude acting on something, but I need to go in reverse.

Say I know there are a slew of charges and the center one feels a force of some magnitude and there is one undefined vector (magnitude and angle unknown) I would think if you know the overall vector, one could calculate the missing vector in terms of magnitude and angle.

I want to solve for this unknown vector but I have no idea how. It seems impossible.

Working with vectors is essential in both mathematics and physics. Here is an intro and some exercises to test your knowledge...courtesy of PF :wink:

Here You Go

regards
marlon
 
  • #9
Thanks for all the help. I guess not having an overall angle made the problem, well, impossible. Including it brought me quickly to the answer.
 

1. What is an Impossible Vector Problem?

An Impossible Vector Problem is a mathematical problem that involves finding a vector (a quantity with both magnitude and direction) that satisfies certain conditions. It is called "impossible" because there is no solution that can satisfy all the conditions at the same time.

2. What causes an Impossible Vector Problem?

An Impossible Vector Problem is usually caused by having too many or conflicting conditions. In other words, the conditions are not consistent with each other and therefore, there is no single vector that can satisfy all of them.

3. How do you know if a vector problem is impossible?

You can determine if a vector problem is impossible by checking if the conditions are consistent with each other. If there is no vector that can satisfy all the conditions, then the problem is impossible.

4. Can an Impossible Vector Problem be solved?

No, an Impossible Vector Problem cannot be solved because there is no single vector that can satisfy all the conditions. However, it is still important to study and understand these types of problems as they can help us identify inconsistencies and improve our problem-solving skills.

5. What can I do if I encounter an Impossible Vector Problem?

If you encounter an Impossible Vector Problem, you can try to simplify the conditions or re-evaluate the problem to see if there are any inconsistencies. If you are unable to find a solution, it is important to seek help from a teacher or a peer who may have a different perspective on the problem.

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