NVAMediumJEE Main 2023 · 6 April, Shift 2Equation of Line in 3D

Mathematics Question from JEE Main 2023 · 6 April, Shift 2

If the lines x12=2y3=z3α\dfrac{x-1}{2} = \dfrac{2-y}{-3} = \dfrac{z-3}{\alpha} and x45=y12=zβ\dfrac{x-4}{5} = \dfrac{y-1}{2} = \dfrac{z}{\beta} intersect, then the magnitude of the minimum value of 8αβ8\alpha\beta is _____ :

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