Question

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

Answer 1

\[\text{ Let the equation of a plane parallel to the given plane be} \]

\[3x + 2y - z = k . . . \left( 1 \right)\]

\[\text{ This passes through (2, -1, 1) So } ,\]

\[3 \left( 2 \right) + 2 \left( - 1 \right) - \left( 1 \right) = k\]

\[ \Rightarrow k = 3\]

\[\text{ Substituting this in (1), we get } \]

\[3x + 2y - z = 3, \text{ which is the equation of the required plane } .\]