Points $A,B,$ and $C$ have position vectors $$A = \left[\begin{array}{cc}a\\b\\c\end{array}\right]$$ $$B = \left[\begin{array}{cc}d\\e\\f\end{array}\right]$$ $$C = \left[\begin{array}{cc}g\\h\\i\end{array}\right]$$ Find the position vector for point $D$ such that $ABCD$ is a parallelogram.
I have been able to do it when numbers are given for $a$ to $i$, but am struggling in this case.
Notation: $IJ$ denotes the vector from point $I$ to point $J$. $O$ is the origin.
You would like to find $OD$. You have $OA$, $OB$, and $OC$. Now simply note that $AB=DC$ and $BC=AD$.
Can you take it from here?