Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r=(3+t) i+(2t-1) j+(2t+4) k and L₃: r=(3+2s) i+(3+2s) j+(2+s) k, t,s. If (a,b,c), a, is the point on L₃ at a distance of √(17) from the point of intersection of L₁ and L₂, then (a+b+c)² is equal to _ _ _.

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 8 Apr, Evening shift · Q23

JEE Main 20268 Apr, Evening shiftMathematicsHardThree Dimensional Geometry249× since 2002

Let a line

L_1

pass through the origin and be perpendicular to the lines

L_2:\vec r=(3+t)\hat i+(2t-1)\hat j+(2t+4)\hat k

and

L_3:\vec r=(3+2s)\hat i+(3+2s)\hat j+(2+s)\hat k

t,s\in\mathbb{R}

. If

(a,b,c)

a\in\mathbb{Z}

, is the point on

L_3

at a distance of

\sqrt{17}

from the point of intersection of

L_1

and

L_2

, then

(a+b+c)^2

is equal to ______.

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