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Prove that the resultant of two force...

Prove that the resultant of two forces acting at point O and represented by ` vec O B` and ` vec O C` is given by 2` vec O D` ,where D is the midpoint of BC.

Text Solution

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`vecR=vec(OB)+vec(OC)`
`" "=(vec(OD)+vec(DB))+(vec(OD)+vec(DC))`
`" "=2vec(OD)+(vec(DB)+vec(DC))=2vec(OD)+vec0=2vec(OD)`
(Since `D` is the midpoint of `BC`, we have `vec(DB)=-vec(DC)`)
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