Give a parametric representation of the line (D) passing through A(1,2,3) and directed by vector u(2, -2, -1).

The line $(D)$ passes through point $A(1,2,3)$ and is directed by the vector $\vec{u}(2, -2, -1)$.
The parametric equations of a line passing through $(x_0, y_0, z_0)$ with direction vector $(a, b, c)$ are:

Substituting the given values $A(1,2,3)$ and $\vec{u}(2, -2, -1)$:

where $t \in \mathbb{R}$.

The direction vector of line $(D)$ is $\vec{u}(2, -2, -1)$.