Question

Write the equation of the plane passing through (2, −1, 1) and parallel to the plane 3x + 2y −z = 7.

Answer 1

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