If ` vec a ,\ vec b ,\ vec c` are the position vectors of the vertices of an equilateral triangle whose orthocentre is the origin, then write the value of ` vec a+ vec b+ vec c`

Explanation

Given,` vec a ,\ vec b ,\ vec c`
are the position vectors of the vertices of an equilateral triangle.

Its centroid`=(vec a+vec b+vec c)/3`

The orthocenrer of an equilateral triangle coincides with its centroid.

`therefore (vec a+vec b+vec c)/3=0`

`implies vec a+vec b+vec c=0`