Q.If G is the centroid of the triangle ABC, then prove by the vector method that GA⃗ + GB⃗ + GC⃗ = 0⃗.

Standard definition from the Vector Algebra chapter.

Given a fixed point $O$ (the origin) in space, the position vector of any point $P$ is the vector $\overrightarrow{OP}$ joining the origin $O$ to $P$. If $P$ has coordinates $(x,y,z)$, its position vector is $x\hat i+y\hat j+z\hat k$; every point in space then corresponds uniquely to its …

definition recall

If $P$ is a point in space with coordinates $(x,y,z)$ relative to an origin $O$, then the vector $\overrightarrow{OP}=x\hat i+y\hat j+z\hat k$ is called the position vector of $P$. …