JEE Main20257 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x 1 = y = z-5 1 is 5 6 , then the sum of all possible values of is

Options

A3 2
B- 3 2
C3
D-3

Correct answer

D. -3

Step-by-step solution

aligned & L₁: x-1 2 = y-2 3 = z-3 4 & L₁: x 1 = y = z-5 1 & x = | array ccc i & j & k 2 & 3 & 4 1 & & 1 array |= i (3-4 )- j (-2)+ k (2 -3) & S.D. = | BA n | n | |= | ( i +2 j -2 k ) n | n | | & 6(13-8 )^2=25 ((4 -3)^2+(2 -3)^2+16 ) & 6 (64 a^2-280 +169 )=25 (20 ^2-36 +34 ) & 116 ^2+348 -164=0 & ₁+ ₂= -348 116 =-3 aligned

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