I need help with the following questions from which I'm asked to solve. My book gives a very brief illustration of moments associated with vectors but with no aided worked problems.
The question (s) :
A force of magnitude 3 units acts at the point with coordinates (1,2,3). The force is applied in the direction of the vector 3i - j + 4k.
i) Find the moment of the force about O (the origin)
ii) What is the moment of the force about the point with coordinates (1,2,3)
iii) Use a diagram to illustrate your answer
For the moment around the origin (0), I've got :-
Unfortunately I don't know how to construct matrices using Latex, so for this reason the following result below is after the determinant (s) have been computed.
Is this correct?
Now for (ii), the formula I've got is :-
Where r is the components of the position vector for the intial point the force is acting.
Now the point where the force is acting is equal to the point where I'm asked to take the moment. I'm confused. If I go buy the aforementioned equation for (ii), then this tells me the moment equates to zero? Could someone please confirm this.
How do I illustrate these results by means of a diagram?
Sidenote - Why have I been given the magnitude of the force as 3 units? As far as I'm concerned I don't even seem to need this, except to illustrate the magnitude in the diagram?