Statics problem, finding the moment (torque) about a straight line

[TPMF]

1. Determine the magnitude and direction of the moment of the vertical 800 lb force about the straight line through points C and D. (See attachment for diagram)



2. I believe that the equation i need is (Moment vector)=(unit vector)*((position vector)X(Force Vector))



3. I feel that I working myself into a dead end. But, I think that The unit vector is 0.164i+0.986j+0k and the force vector is 0i-800j+0k
I am having trouble finding what the position vector needs to be, though as I said earlier, I think i am going about this the wrong way.

 

[SteamKing]

You might review how to calculate a moment about an arbitrary axis:

http://classes.uleth.ca/200803/engg2000a/Fri%20Oct%203.pdf

 

[voko]

Your unit vector is wrong. The CD line is in the XZ plane, so its unit vector cannot have a component in the Y direction (j).

As for the position vector, recall that it is a vector form any point on the axis to any point on the line of force.

 

[TPMF]

Thank you SteamKing and voko.
I did not realize that the position vector could be any two points, as long as they are along the line of force and the CD line. Also, thank you for pointing out my error with the unit vector, I switched the y and z values since i am use to a different orientation of the z axis.

What i ended up getting was:
u= <0.164, 0, 0.986>
r= <1.5, -3, -1>
F <0, 800, 0>

M = u*(r×F)
M = 0.164(800)-0(0)+0.986(1200)
M = 1314.4 lb-ft

I think that is correct, but do let me know if you see a mistake.
And, thank you both again.