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Question Id : 14467 | Context : JEE Main 2024 (8 April Morning Shift)
$L_1:;\vec r=(2+\lambda),\hat i+(1-3\lambda),\hat j+(3+4\lambda),\hat k,;\lambda\in\mathbb R$ $L_2:;\vec r=2(1+\mu),\hat i+3(1+\mu),\hat j+(5+\mu),\hat k,;\mu\in\mathbb R$ is $\dfrac{m}{\sqrt{n}}$, where $\gcd(m,n)=1$, then the value of $m+n$ equals


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