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if vec Ao + vec O B = vec B O + vec ...

if ` vec Ao` + ` vec O B` = ` vec B O` + ` vec O C` ,than prove that B is the midpoint of AC.

Text Solution

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`vec(AO)+vec(OB)=vec(BO)+vec(OC)`
`rArr" "vec(AB)=vec(BC)`
Thus, vectors `vec(AB)and vec(BC)` are collinear
`rArr" "` Points A, B, C are collinear
Also `" "|vec(AB)|=|vec(BC)|`
`rArr" "B` is the midpoint of `AC`
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