How do I determine the line of action for calculating a moment in 3D space?

[salman213]

When taking the moment in 3 space i know the formula is

M = r x F


but for example ifyour finding the moment of force F about point C


how do u know from point C to where you have to make the line.

like if u have

------------------> about point C

C

you can make it

------------------> F
-a
-
C

or 

------------------>F
                -a
           -
      -
C

Ive read that the ca is a vector from point C to ANYWHERE on the line of action. So does that mean any where from point C to the line F ANYWHERE?

 

[Pyrrhus]

Yes, that's correct.

 

[piercas]

I would recommend using a systematic approach to determine the line of action for calculating a moment in 3D space. This could include the following steps:

1. Identify the point of interest (in this case, point C) and the force vector (F) for which you want to calculate the moment.

2. Draw a diagram or visualize the setup in 3D space to better understand the orientation of the force and the point of interest.

3. Use the formula M = r x F to calculate the moment, where r is the position vector from the point of interest (C) to any point on the line of action of the force.

4. To determine the line of action, you can use the position vector (r) and the direction of the force vector (F) to find the direction of the line of action. This can be done by using vector addition or subtraction.

5. Once you have the direction of the line of action, you can determine the exact location on the line by using the magnitude of the position vector (r) and the direction of the line of action.

It is important to note that the position vector (r) can be any vector from the point of interest (C) to any point on the line of action. This means that the line of action can be determined from any point on the line, as long as the direction and magnitude of the position vector is accurate.

In summary, determining the line of action for calculating a moment in 3D space involves understanding the orientation of the force and the point of interest, using the formula M = r x F, and using vector calculations to determine the direction and location of the line of action.