Points $(1, 1, 1), (-2, 4, 1), (-1, 5, 5)$ and $(2, 2, 5)$ are the vertices of a

If the points $P = \hat{i} + 2 \hat{j}$,$Q = 4 \hat{i} + 6 \hat{j}$,$R = 5 \hat{i} + 7 \hat{j}$,and $S = a \hat{i} + b \hat{j}$ are the consecutive vertices of a parallelogram $PQRS$,then:

In a triangle $ABC$, if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively, then $AB^2+BC^2+CA^2=$

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

Three consecutive vertices of a parallelogram $ABCD$ are $A(6, -2, 4)$,$B(2, 4, -8)$,and $C(-2, 2, 4)$. Find the coordinates of the fourth vertex $D$.

If the vertices of a triangle $ABC$ are $A(1, 2, 3)$,$B(h, -3, 0)$,and $C(-4, k, -1)$ and the centroid of the triangle is $\left(5, -1, \frac{2}{3}\right)$,then triangle $ABC$ is