How do I find the intersection of the wrench's LOA?

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SUMMARY

The discussion centers on finding the intersection of a wrench's line of action (LOA) in a three-dimensional space using vector mechanics. The user has calculated the moment vector M = (4.5, 3, -6) using the cross product with position vector r = (0, 0.06, 0.03) m and force vector F = (100, 150, 0) N. To determine the intersection with the yz-plane, the user must apply the formula M = Fd, where d represents the distance from the point of application to the line of action. The conversation emphasizes the need for clarity in vector notation and the importance of visual aids, such as diagrams, for solving the problem.

PREREQUISITES
  • Understanding of vector mechanics and cross products
  • Familiarity with the concept of a wrench and its equivalent force system
  • Knowledge of the formula M = Fd in three-dimensional space
  • Ability to interpret and create diagrams for vector problems
NEXT STEPS
  • Study the application of the cross product in vector mechanics
  • Learn how to derive a wrench equivalent force system
  • Explore the relationship between moments and lines of action in 3D
  • Watch instructional videos on vector mechanics and the line of action concept
USEFUL FOR

Students and professionals in engineering, particularly those focusing on mechanics and structural analysis, will benefit from this discussion. It is especially relevant for those working with forces and moments in three-dimensional systems.

daisy7777
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Homework Statement
A thin rectangular flat plate is loaded by the forces show. Determine a wrench equivalent force system, and specify the y and z coordinates of the point where the wrench's LOA intersects the yz plane.
Relevant Equations
M = Fd
M = r xF
I've solved for the moment using the cross product where my r = 0i+0.06j+0.03k m and my F = 100i + 150j + 0k. I got my moment to be M= 4.5,3,-6. I know a wrench equivalent force must be parallel to the force (I am assuming this means the resultant force in this case), but how do I apply that logic to fid the intersection? I assume I am meant to use the formula M=Fd where F = 300i, 0j, 0k but I am not sure if this is even applicable in this question as it is in 3D.

All in all, I would just like a little push in the right direction.
 
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daisy7777 said:
Homework Statement: A thin rectangular flat plate is loaded by the forces show. Determine a wrench equivalent force system, and specify the y and z coordinates of the point where the wrench's LOA intersects the yz plane.
Relevant Equations: M = Fd
M = r xF

I've solved for the moment using the cross product where my r = 0i+0.06j+0.03k m and my F = 100i + 150j + 0k. I got my moment to be M= 4.5,3,-6. I know a wrench equivalent force must be parallel to the force (I am assuming this means the resultant force in this case), but how do I apply that logic to fid the intersection? I assume I am meant to use the formula M=Fd where F = 300i, 0j, 0k but I am not sure if this is even applicable in this question as it is in 3D.

All in all, I would just like a little push in the right direction.
Since you have not posted the details of the question, it is impossible to check your work. In particular, you do not explain how you obtained that vector for r.
 
@daisy7777, note what @haruspex said in Post #2. And a diagram is needed.

You have written "F = 100i + 150j" + 0k and "F = 300i, 0j, 0". If you are referring to two different forces the meaning of each must be clear and they should have different symbols.

If you are not familiar with the method, try watching the short (~5 mins) video here
 

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