Tetrahedron

Q.

If $A,B$ and $C$ are the vertices of a triangle whose position vectors are $a,b$ and $c$ respectively and $G$ is the centroid of the $∆ABC$, then $GA+GB+GC$ is?

1. $0$

2. $a+b+c$

3. $\frac{(a+b+c)}{3}$

4. $\frac{(a-b-c)}{3}$

Q. A plane passing through $(1,1,1)$ cuts positive direction of coordinate axes at $A,B$ anc $C,$ then the volume of tetrahedron $OABC$ satisfies

1. $V\le \frac{9}{2}$
2. $V\ge \frac{9}{2}$
3. $V=\frac{9}{2}$
4. none of these

Q. The co-ordinates of the vertices of the given tetrahedron are (1, 2, 3), (5, 8, 6), (14, 15, 18) and (0, 0, 0). Find the co-ordinates of the centroid of the tetrahedron?

1. (5, 7, 6)
2. (5, 6.25, 6.75)
3. (7, 5, 6)
4. (6.67, 8.34, 9)