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MathsJEE Main 8 Apr 2026, Shift 2·Q23·Numerical·Moderate

3D Geometry · Line perpendicular to two lines

Let a line L1L_1 pass through the origin and be perpendicular to the lines
L2:r⃗=(3+t)i^+(2t−1)j^+(2t+4)k^andL3:r⃗=(3+2s)i^+(3+2s)j^+(2+s)k^,\begin{align*} L_2 &: \vec r = (3 + t)\hat i + (2t - 1)\hat j + (2t + 4)\hat k \quad\text{and}\\ L_3 &: \vec r = (3 + 2s)\hat i + (3 + 2s)\hat j + (2 + s)\hat k, \end{align*}
t,s∈Rt, s \in \mathbb{R}. If (a,b,c)(a, b, c), a∈Za \in \mathbb{Z}, is the point on L3L_3 at a distance of 17\sqrt{17} from the point of intersection of L1L_1 and L2L_2, then (a+b+c)2(a + b + c)^2 is equal to .

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