The distance between the line r = 2 i - 2 j + 3 k + λ (i - j + 4k), and the plane r.(i + 5 j + k) = 5 is

Three Dimensional Geometry: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q2389

JEE Main 2005Annual, Paper 1MathematicsEasyThree Dimensional Geometry249× since 2002

The distance between the line

\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),

and the plane

\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5

JEE Main 2005 · Annual, Paper 1 · Q2389

JEE Main 2005Annual, Paper 1MathematicsEasyThree Dimensional Geometry249× since 2002

The distance between the line

\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),

and the plane

\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5