If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines (x + 1)/2 = (y - 3)/4 = (z + 1)/3 and (x + 3)/2 = (y + 2)/6 = (z - 1)/(λ)(λ R) is equal to k/(√(633)), then k is equal to _ _ _.

Three Dimensional Geometry: JEE Main 2020 Mathematics question

JEE Main 2020 · 9 Jan, Evening shift · Q18

JEE Main 20209 Jan, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines

{{x + 1} \over 2} = {{y - 3} \over 4} = {{z + 1} \over 3}

and

{{x + 3} \over 2} = {{y + 2} \over 6} = {{z - 1} \over \lambda }\left( {\lambda \in R} \right)

is equal to

{k \over {\sqrt {633} }}

, then k is equal to ______.

Your answerType your answer. Integers and decimals are accepted.