MathematicsMedium249×since 2002Q2538If the shortest distance between the lines L1:r⃗=(2+λ)i^+(1−3λ)j^+(3+4λ)k^,λ∈RL2:r⃗=2(1+μ)i^+3(1+μ)j^+(5+μ)k^,μ∈R\begin{array}{ll} L_1: \vec{r}=(2+\lambda) \hat{i}+(1-3 \lambda) \hat{j}+(3+4 \lambda) \hat{k}, & \lambda \in \mathbb{R} \\ L_2: \vec{r}=2(1+\mu) \hat{i}+3(1+\mu) \hat{j}+(5+\mu) \hat{k}, & \mu \in \mathbb{R} \end{array}L1:r=(2+λ)i^+(1−3λ)j^+(3+4λ)k^,L2:r=2(1+μ)i^+3(1+μ)j^+(5+μ)k^,λ∈Rμ∈R is mn\frac{m}{\sqrt{n}}nm, where gcd(m,n)=1\operatorname{gcd}(m, n)=1gcd(m,n)=1, then the value of m+nm+nm+n equalsA384B387C390D377Check answerSkip