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