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JEE Main20244 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines x+2 2 = y+3 3 = z-5 4 and x-3 1 = y-2 -3 = z+4 2 is 38 3 5 k , and ₀^ k [x^2 ] d x= - , where [x] denotes the greatest integer function, then 6 ^3 is equal to________

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aligned & 38 3 5 k = (5 i +5 j -9 k ) 5 | array ccc i & j & k 2 & 3 & 4 1 & -3 & 2 array | & 38 3 5 k = 19 5 & k = 19 5 & k = 3 2 & ₀^ 3 / 2 [ x ^2 ]= ₀^1 0+ ₁^ 2 1+ _ 2 ^ 3 / 2 2 & = 2 -1+2 ( 3 2 - 2 ) & =2- 2 & =2 & 6 ^3=48 aligned

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