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प्रश्न
If point C `(barc)` divides the segment joining the points A(`bara`) and B(`barb`) internally in the ratio m : n, then prove that `barc=(mbarb+nbara)/(m+n)`
उत्तर
Given that C`(vecc)` divides the segment joining the points A `(veca)` and B `(vecb)`
internally in the ratio m : n
We need to prove that `vecc=(mvecb+nveca)/(m+n)`
Consider the following figure
since `(`
n x length (AC)=m X length (BC)
`nvec(AC)=mvec(CB)`
`n(vec(OC)-vec(OA))=m(vec(OB)-vec(OC))`
`n(vecc-veca)=m(vecb-vecc)`
`nvecc-nveca=mvecb-mvecc`
`(n+m)vecc=mvecb+nveca`
`vecc=(mvecb+nveca)/(m+n)`
Hence proved.
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