Question

Find the equation of the plane which is parallel to 2x − 3y + z = 0 and which passes through (1, −1, 2).

Answer 1

$$\begin{gathered} \text{Let the equation of a plane parallel to the given plane be} \\ 2x-3y+z=k...\left(1\right) \\ \text{This passes through (1, -1, 2).\hspace{0.17em}So,} \\ 2\left(1\right)-3\left(-1\right)+\left(2\right)=k \\ \Rightarrow k=7 \\ \text{Substituting this in (1), we get} \\ 2x-3y+z=7,\text{which is the equation of the required plane.} \end{gathered}$$