Let G be the centroid of ΔABC and S be any point in the plane of a ΔABC.

Statement-1: $\vec{SA} + \vec{SB} + \vec{SC} = 3 \vec{SG}$

Statement-2: If O, A and B are three points in a plane, then $m\vec{OA}+n\vec{OB} = (m + n)\vec{OC}$, where C is a point dividing AB in the ratio $n : m$.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Let O be the origin.

Using section formula, we have

$\vec{OC}=\frac{n\vec{OB}+m\vec{OA}}{n+m}⇒ (m+n)\vec{OC}=m\vec{OA}+n\vec{OB}$

So, statement-2 is true.

Now,

$\vec{SA} + \vec{SB} + \vec{SC} =\vec{SA}+(\vec{SB} + \vec{SC})$

$⇒\vec{SA} + \vec{SB} + \vec{SC} =\vec{SA}+2\vec{SD}$  [Using statement-2 for m = n = 1]

$⇒\vec{SA} + \vec{SB} + \vec{SC} =(1+2)\vec{SG}$   [Using statement-2]

$⇒\vec{SA} + \vec{SB} + \vec{SC} =3\vec{SG}$

So, both the statements are true and statement-2 is a correct explanation for statement-1.