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3D Geometry question

2024 · 8 Apr · Shift 1 · Q49

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JEE Main
Mathematics
3D Geometry
2024 · 8 Apr · Shift 1 · Q49

3D Geometry question

2024 · 8 Apr · Shift 1 · Q49

JEE MainMathematics3D GeometryMCQ+4 / −1

If the shortest distance between the lines

\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}

is

\frac{m}{\sqrt{n}}

, where

\operatorname{gcd}(m, n)=1

, then the value of

m+n

equals

A
384
B
387
C
390
D
377

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