Given the plane (1) x+2y+3z=0 in ${{R}^{3}}$ And a point $M({{x}_{0}},{{y}_{0}},{{z}_{0}})$in ${{R}^{3}}$not in the plane (1). Find the projection of the point M onto the plane (1) And explain why the orthogonal projection of a point in a plane is a linear transformation.
I found the Parametric equations of the line that passes through point and its projection .Why this is a linear transformation?
$\begin{align} & {{x}_{0}}^{\prime }={{x}_{0}}+t \\ & {{y}_{0}}^{\prime }={{y}_{0}}+2t \\ & {{z}_{0}}^{\prime }={{z}_{0}}+3t \\ \end{align}$