If the shortest distance between the lines (x - 1)/2 = (y - 2)/3 = (z - 3)/(λ) and (x - 2)/1 = (y - 4)/4 = (z - 5)/5 is 1/(3), then the sum of all possible value of λ is:

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Evening shift · Q2504

JEE Main 202224 Jun, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

{{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}

{1 \over {\sqrt 3 }}

, then the sum of all possible value of

\lambda

is :

JEE Main 2022 · 24 Jun, Evening shift · Q2504

JEE Main 202224 Jun, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

{{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}

{1 \over {\sqrt 3 }}

, then the sum of all possible value of

\lambda

is :