Question

If A, B, C are the vertices of a triangle whose position vectors are `overline("a"),overline("b"),overline("c")` and G is the centroid of the `triangle ABC,` then `overline("GA")+overline("GB")+overline("GC")` is ______.

पर्याय

• `overline(0)`

• `overline(a)+overline(b)+overline(c)`

• `(overline("a")+overline("b")+overline("c"))/3`

• `(overline("a")+overline("b")-overline("c"))/3`

Answer 1

If A, B, C are the vertices of a triangle whose position vectors are `overline("a"),overline("b"),overline("c")` and G is the centroid of the `triangle ABC,` then `overline("GA")+overline("GB")+overline("GC")` is `overline(0)`.

Explanation:

`overline("GA")+overline("GB")+overline("GC")=(overline("a")-overline("g"))+(overline("b")-overline("g"))+(overline("c")-overline("g"))`

`=overline("a")+overline("b")+overline("c")-3overline("g")`

`=overline("a")+overline("b")+overline("c")-3((overline("a")+overline("b")+overline("c"))/3)=overline(0)`