Points and vectors

In a triangle $ABC$, let $K$, $L$ and $M$ be the midpoints of $AB$, $BC$ and $AC$ consecutively and let $T$ be the centroid of $ABC$. Find the values of coefficients $k$, $l$ and $m$ if: $$\overrightarrow{TM}=k\cdot \overrightarrow{BT};\overrightarrow{ML}=l\cdot \overrightarrow{BA};\overrightarrow{CK}=m\cdot \overrightarrow{TC}$$

Let there be a triangle KLM and vectors $\overrightarrow{a}$, $\overrightarrow{c}$ in the coordinate system. Triangle $KLM$ and vectors $\overrightarrow{a}$, $\overrightarrow{c}$ are given in the coordinate system shown in the picture. Point T is the centroid of the triangle KLM. Express vector $\overrightarrow{x}$, where $\overrightarrow{x}=\overrightarrow{KT}$ as a linear combination of $\overrightarrow{a}$ and $\overrightarrow{c}$ and evaluate $\left|\overrightarrow{x}\right|$.

We are given points $A=[2;1]$, $B=[4;-1]$, and $T=[6;2]$, where point $T$ is the centroid of triangle $ABC$. Find the coordinates of $C$, which is the vertex of $ABC$.

We are given points $A=[1;-1;2]$, $B=[0;5;-3]$, $S=[2;0;5]$. Point $S$ is the centre of a parallelogram $ABCD$. Find the coordinates of vertices $C$ and $D$.