The points $(2, 3, 4)$,$(-1, -2, 1)$,and $(5, 8, 7)$ are

If the three vertices of a parallelogram are $(-1, 0), (3, 1),$ and $(2, 2)$ respectively,find the coordinates of the fourth vertex.

Verify that the points $(0, 7, -10)$,$(1, 6, -6)$,and $(4, 9, -6)$ are the vertices of an isosceles triangle.

If the midpoints of the sides $AB$,$BC$,and $CA$ of a triangle are respectively $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$,then the centroid of the triangle $ADF$ is

$\triangle ABC$ has vertices at $A \equiv (2, 3, 5)$,$B \equiv (-1, 3, 2)$ and $C \equiv (\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the axes,then the values of $\lambda$ and $\mu$ respectively are

$A(3, 2, -1), B(4, 1, 1), C(6, 2, 5)$ 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