Why are the resulting moment and force vectors collinear?

[d5c1d6d65]

hello,

I would like you to take a look at the picture below. My question is why it is states that de resulting moment vector is collineair with the force vector...

This is my method to solve this kind of problems:
*determine the moment about the three axis => than we now the 3 components of the resulting moment vector
*determine the resulting force vector
* definiton of moment = vector product = rxM , with r the position (x;y)

What do I do wrong?

thank you vm !

 

[d5c1d6d65]

someone can give an explanation ?

thank you vm

 

[Camille]

The moment of the wrench always lies on the same central axis as the resultant force.
The wrench can be applied when FR$$\bullet$$M$$\neq$$0. That practically means that FR is never perpendicular to moment.
Finding the wrench means to find an axis at which the perpendicular component of moment is zero (so we are only left with the parallel component).