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

[daisy7777]

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.

 

[haruspex]

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.

 

[berkeman]

the point where the wrench's LOA

Sorry, what is LOA in this context?

https://www.abbreviations.com/LOA

 

[Steve4Physics]

Sorry, what is LOA in this context?

https://www.abbreviations.com/LOA

Line of action.

 

[Steve4Physics]

@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