the attached file is an old exam my professor sent out. i my struggles were with 2 and 3. number 2: I am having trouble calculating the moments and picking a vector for r in the equation M=r x F which reads the cross product of the r and F vectors. Also to find the thetas, for part 2, can I use the dot product to find the angle between them and thus theta?
For problem 2, r is just the distance from O to a point in the line of action of force F. In other words, this is just the distance from O to B. I believe this is <4, -3, 1.5>. I'm not sure as to how you would use a dot product to find theta x, y, and z. However, the easiest solution here is to break your force F down into components (ijk form). You can do this by taking F times the unit vector of the force. The unit vector is just the direction components of the force divided by the magnitude of the direction components. In other words: F[(4/[tex]\sqrt{106}[/tex])i - (3/[tex]\sqrt{106}[/tex] )j - (9/[tex]\sqrt{106}[/tex] )k] This will give you distinct F_{x}, F_{y}, and F_{z} components for the force F and you can find theta_{x}, theta_{y}, and theta_{z} forms by: theta_{x} = cos^{-1}(F_{x}/F) theta_{y} = cos^{-1}(F_{y}/F) theta_{z} = cos^{-1}(F_{z}/F) I hope this helps. :)
thanks. I sort of figured it out after consulting a friend. To calculate the moment you evaluate a determinant of i,j,k being the first row, r components being the second, and F components being the third. As for the thetas, find the unit vector and set the components equal to arccosine like you said. This way is a bit easier because the hypotenuse is 1. This seems to be the correct way to do it.