Posted by Aaron on .
Calculate the moment about a point (5; 4; 3) ft. caused by the forces
P = 3^i  2^j  4^k lb. and Q = 5^i + 7^j  2^k lb. acting at the points
(7; 2; 2) ft. and (3; 2; 5) ft., respectively.
What I did was this;
vector r1= (7,2,2)  (5,4,3) = 2i2j5k
vector r2= (3,2,5)  (5,4,3) = 8i6j+2k
Vector M1= (2i2j5k) X P = 7i7j+2k
Magnitude= 7.55 ftlbs
Vector M2= (8i6j+2k) X Q = 2i6j+85k
Magnitude= 86.23 ftlbs
Moment about the given point = (7.55) + (86.23) = 93.78 ftlbs
I'm unsure if this is right
No one has answered this question yet.

Engineering 
drwls,
You seem to have dropped some minus signs, but then corrected the errors.
vector r1= (7,2,2)  (5,4,3) = 2i2j5k
vector r2= (3,2,5)  (5,4,3) = 8i6j+2k
I do not agree with your cross products.
M1 should be
 i j k
2 2 5
3 2 4
The i component is 8 10 = 2
The j component is 15 +8 = 7
The k component is 4 +6 = 2
Are you sure you didn't mean M1 = 2i 7j +2k ?
The magnitude of 7i7j+2k would not be 7.55.
So far, You seem to be going about it the right way but making typo errors.
For the total moment about the point, subtract the components first. Then take the sqrt of the sum of the squares of the differences. That is not what you did. You added magnitudes of vectors that are not parallel.
Thanks you for showing your work. I wish more students would do that. 
Engineering 
Aaron,
Thank you, I reevaluated my work and found all the errors.
Though I'm not sure sure why you would subtract M1 and M2 if you are looking for the total force applied?
Wouldn't M1 + M2 make more sense in this case? 
Engineering 
Aaron,
Such as (2i7k+2k) + (2i6j+26k)?
To get to get my final vector in which I take the squareroot of the sum of the squares?
Also thanks I didn't recognize my conceptual error.
But I still believe it would be M1 + M2. 
Engineering 
drwls,
You cannot algebraically add magnitudes unless they are in the same direction. M1 and M2 are not.
Add the two moments as vectors and THEN compute the magnitude.