How to Calculate Moment of a Couple Using Cross Products?

[lc99]

Homework Statement

Homework Equations

The Attempt at a Solution

I am confused. It looks like the couple forces are at a angle pointing to the x axis.
So i did moment about a axis of that angle.

I found this angle/axis unit vector to be (-0.6i -0.8j)
Then i found the moment couple about the x and y-axis and the magnitude is 3663.

Multiplied it by the unit vector and found its magnitude as 3663. However the answer is not in the choice!

 

[Dr Dr news]

We know the couple/moment/torque is r x F and the direction is ccw from the sketch thus you can eliminate e) and f). So you just need to find the x and y components of each r and F, take the cross products and sum them.

 

[lc99]

We know the couple/moment/torque is r x F and the direction is ccw from the sketch thus you can eliminate e) and f). So you just need to find the x and y components of each r and F, take the cross products and sum them.

Quick question. I am working on another problem and it is killing me...

I keep getting 5/2 and the answer should be e. 5/4m/

I found that Fr = -4F1
and Moment about the left point is -10F1

so M = F*d --> d = 5/2 or x=5/2
but it is not right??

 

[haruspex]

So i did moment about a axis of that angle.

I do not know what that means. Please explain.

Then i found the moment couple about the x and y-axis and the magnitude is 3663.

Can't tell where you went wrong without seeing the details.
Further Dr Dr news' post, you can choose what point you take along the line of action of each force as the point of application. You can do this in such a way that only one of the two components has a moment about the axis.

Im working on another problem and it is killing me...

Please post a new thread - as per forum style.

 

[Dr Dr news]

Back to the original problem. Find r(A) = - 8 i + 8 j and F(A) = - 72 i + 96 j. Then do the same for r(B) and F(B). Take the cross products r x F for each of A and B and sum them.