The quadrilateral formed by the points $A(1,2,5), B(-1,6,1), C(3,4,-3)$ and $D(5,0,1)$ is a

Find the third vertex of a triangle whose centroid is the origin and two vertices are $(2, 4, 6)$ and $(0, -2, -5)$.

Given $\triangle ABC$ such that $A = 2\hat{i} - \hat{j} + \hat{k}$,$B = \hat{i} - 3\hat{j} - 5\hat{k}$,and $C = 3\hat{i} - 4\hat{j} - 4\hat{k}$,then $\triangle ABC$ is:

The centroid of a triangle $ABC$ is at the point $(1,1,1)$. If the coordinates of $A$ and $B$ are $(3,-5,7)$ and $(-1,7,-6)$ respectively,find the coordinates of the point $C$.

$A(3, 2, -1), B(4, 1, 1), C(6, 2, 5)$ are three points. If $D, E, F$ are three points which divide $BC, CA, AB$ respectively in the same ratio $2: 1$,then the centroid of $\triangle DEF$ is

If the centroid of the triangle whose vertices are $(a, 1, 3)$,$(-2, b, -5)$,and $(4, 7, c)$ is the origin,then the values of $a, b, c$ are: