If the straight lines x-1 k = y-2 2 = z-3 3 and x-2 3 = y-3 k = z-1 2 intersect at a point, then the integer k is equal to

Step-by-step solution

When the two lines intersect then shortes distance between them is zero i.e. aligned & ( a ₂- a ₁ ) b ₁ b ₂ | b ₁ b ₂ | =0 & ( a ₂- a ₁ ) b ₁ b ₂=0 aligned where a ₁= i +2 j +3 k , b ₁=k i +2 j +3 k aligned & a ₂=2 i +3 j + k , b ₂=3 i +k j +2 k & | array ccc 1 & 1 & -2 k & 2 & 3 3 & k & 2 array |=0 & 1(4-3 k)-1(2 k-9)-2 (k^2-6 )=0 & -2 k^2-5 k+25=0 k=-5 or 5 2 aligned