a force of 8kg acts through the point 4,-1,7 in the direction of 6i+9j-2k find the moment of the force about the point 1,-3,2
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Answer....
The unit vectors in the direction of the given vectors are
36+4+9
6i+2j+3k= 7
6i+2j+3k 7
3i−2j+6k
and
7
2i−3j−6k
Since F
1
,F
2
and F
3
are the forces of magnitude 5,3 and 1 units, we have
F
1
=
7
5
(6i+2j+3k),
F
2
=
7
3
(3i−2j+6k),
F
3
=
7
1
(2i−3j−6k),
Therefore the resultant is
R=F
1
+F
2
+F
3
=
7
1
(41i+j+27k) and AB=3i+4k.
Hence the work done is R⋅AB=
7
1
(41×3+27×4)=
7
231
=33 units.
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