Find the equation of the plane passing through point (1, 1, 1) and parallel to the plane x + 2y + 3z – 7 = 0

Given plane is x + 2y + 3z – 7 = 0

compare with ax+by+cz+d=0
Where a = 1, b = 2, c = 3
Given point (x₁, y₁, z₁) = (1,1,1)
Equation of plane passing through (x₁, y₁, z₁) and parallel to the plane ax + by + cz + d = 0 is
$\begin{array}{l}\mathrm{a}\left(\mathrm{x}-{\mathrm{x}}_1\right)+\mathrm{b}\left(\mathrm{y}-{\mathrm{y}}_1\right)+\mathrm{c}\left(\mathrm{z}-{\mathrm{z}}_1\right)=0\\ \mathrm{x}-1+2\mathrm{y}-2+3\mathrm{z}-3=0\\ \Rightarrow \mathrm{x}+2\mathrm{y}+3\mathrm{z}-6=0\end{array}$