If the three consecutive vertices of a parallelogram are $A(1, 2, 3)$,$B(-1, -2, -1)$,and $C(2, 3, 2)$,then its fourth vertex is:

For $a \neq 0$,if the sum of the distances of a point $P(x, y, z)$ from the points $F_1(a, 0, 0)$ and $F_2(-a, 0, 0)$ is a constant $2k$,then the locus of that point is

$A(2,3,-4), B(-3,3,-2), C(-1,4,2)$ and $D(3,5,1)$ are the vertices of a tetrahedron. If $E, F, G$ are the centroids of its faces containing the point $A$, then the centroid of the triangle $EFG$ is

If the vertices of $\Delta ABC$ are $(a, 0, 0)$,$(0, b, 0)$,and $(0, 0, c)$ respectively,then $\angle B = \dots$

Three identical balls of radius $2 \, cm$ each are placed on a table such that they touch each other as well as the table. Now a fourth ball of the same radius is placed above these three balls. The height of the highest point on the fourth ball above the table is -

If $\left(\frac{9}{4}, \frac{5}{4}, \frac{15}{4}\right)$ is the centroid of a tetrahedron whose vertices are $(a, 2, 1), (1, b, 4), (4, 0, c)$ and $(1, 1, 7)$, then