If the shortest distance between the lines (x - 1)/2 = (y - 2)/3 = (z - 3)/4 and x/1 = y/(α) = (z - 5)/1 is 5/(√(6)), then the sum of all possible values of α is:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q177

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

\frac{x}{1} = \frac{y}{\alpha} = \frac{z - 5}{1}

\frac{5}{\sqrt{6}}

, then the sum of all possible values of

\alpha

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q177

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

If the shortest distance between the lines

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

and

\frac{x}{1} = \frac{y}{\alpha} = \frac{z - 5}{1}

\frac{5}{\sqrt{6}}

, then the sum of all possible values of

\alpha

is: