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

Step-by-step solution

The shortest distance between the lines x-1 2 = y-2 3 = z-3 and x-2 1 = y-4 4 = z-5 5 is d = | | array ccc x₂-x₁ & y₂-y₁ & z ₂- z ₁ a ₁ & ~b ₁ & c ₁ a ₂ & ~b ₂ & c ₂ array | ( a ₁ ~b ₂- a ₂ ~b ₁ )^2+ ( a ₁ c ₂- a ₂ c ₁ )^2+ ( b ₁ c ₂- b ₂ c ₁ )^2 | d= | | array lll 1 & 2 & 2 2 & 3 & 1 & 4 & 5 array | (8-3)^2+(10- )^2+(15-4 )^2 | aligned & 1 3 = | 5-2 17 ^2-140 +350 | & 1 3 = 25-20 +4 ^2 17 ^2-140 +350 & 5 ^2-80 +275=0 & ^2-16 +55=0 & ( -5)( -11)=0 & =5 or =11 aligned Sum of possible values of =16