$A(1,1,1), B(1,-4,3), C(2,-2,0)$ and $D(8,1,4)$ are the vertices of a tetrahedron. $G_1, G_2, G_3$ and $G_4$ are the centroids of the faces $A B C, B C D, C D A$ and $D A B$. Then, the centroid of the tetrahedron having $G_1, G_2, G_3$ and $G_4$ as its vertices is

Let $A(2,3,-1), B(4,1,0), C(-1,-1,1)$ be the vertices of a $\triangle A B C$. Let $D$ be the point where the bisector of $B A C$ meet the side $B C$. Then, the direction ratios of $A D$ are

If a plane passing through the points $(2,3,0),(0,-5,2)$ and ( $-2,0,3$ ) meets the $X, Y$ and $Z$-axes in $A, B$ and $C$ respectively, then $A=$

Let [ $x$ ] denote the greatest integer less than or equal to $x$ and $f(x)=2 x-[2 x]$. If $\mathop {\lim }\limits_{x \to {2^ - }} f(x)=l_1$ and $\mathop {\lim }\limits_{x \to {2^ + }} f(x)=l_2$, then $l_1+l_2=$