If the shortest distance between the lines r = (- i + 3 k) + λ (i - a j) and r = (- j + 2 k) + μ (i - j + k) is √(2/3), then the integral value of a is equal to _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Morning shift · Q23

JEE Main 202224 Jun, Morning shiftMathematicsHardThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

\overrightarrow r = \left( { - \widehat j + 2\widehat k} \right) + \mu \left( {\widehat i - \widehat j + \widehat k} \right)

\sqrt {{2 \over 3}}

, then the integral value of a is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 · 24 Jun, Morning shift · Q23

JEE Main 202224 Jun, Morning shiftMathematicsHardThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

\overrightarrow r = \left( { - \widehat j + 2\widehat k} \right) + \mu \left( {\widehat i - \widehat j + \widehat k} \right)

\sqrt {{2 \over 3}}

, then the integral value of a is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.