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MathsJEE Main 28 Jan 2026, Shift 2·Q24·Numerical·Moderate

3D Geometry · Distance along a given direction

If the distance of the point P(43,α,β)P(43, \alpha, \beta), β<0\beta < 0, from the line r⃗=4i^−k^+μ(2i^+3k^)\vec r = 4\hat i - \hat k + \mu(2\hat i + 3\hat k), μ∈R\mu \in \mathbb{R} along a line with direction ratios 3,−1,03, -1, 0 is 131013\sqrt{10}, then α2+β2\alpha^2 + \beta^2 is equal to .

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