Question

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

Answer 1

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