A line with direction ratios 1,-1,2 intersects the lines x/2=y/3=(z+1)/3 and (x+1)/(-1)=(y-2)/1=z/4 at the points P and Q, respectively. If the length of the line segment PQ is α, then 225α² is equal to:

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Morning shift · Q14

JEE Main 20264 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

A line with direction ratios

1,-1,2

intersects the lines

\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}

and

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

at the points P and Q, respectively. If the length of the line segment PQ is

\alpha

, then

225\alpha^2

is equal to: