Concept:Two intersecting lines must be coplanar. Hence, the shortest distance between them is zero, and the determinant formed by their direction vectors and the vector joining their points must be zero.Explanation:For L1, a point is A(1,2,1) and direction vector is a=⟨2,3,4⟩.For L2, a point is B(3,k,0) and direction vector is b=⟨−1,2,1⟩.Therefore, AB=(3−1,k−2,0−1)=⟨2,k−2,−1⟩.Since the lines intersect, these three vectors must be coplanar.So, the determinant must be zero:22−1k−232−141=0Expanding the determinant:2(3−8)−(k−2)(2+4)+(−1)(4+3)=0−10−6(k−2)−7=0−10−6k+12−7=0−5−6k=0Hence, k=−65.Answer:k=6−5Correct option: A.