Let the line of the shortest distance between the lines L_1: \overrightarrow{r}=(\stackrel{\^}{i}+2 \stackrel{\^}{j}+3 \stackrel{\^}{k})+\lambda(\stackrel{\^}{i}-\stackrel{\^}{j}+\stackrel{\^}{k}) and {\L}_2: { {\r}}^{\to}=(4 \stackrel{\^}{ {\i}}+5 \stackrel{\^}{ {\j}}+6 \stackrel{\^}{ {\k}})+\mu(\stackrel{\^}{ {\i}}+\stackrel{\^}{ {\j}}-\stackrel{\^}{ {\k}}) intersect {\L}_1 and {\L}_2 at {\P} and {\Q} respectively. If (\alpha, \beta, \gamma) is the midpoint of the line segment PQ, then 2(\alpha+\beta+\gamma) is equal to____ [1-Feb-2024 Shift 1]

JEE Main 1-Feb-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 29 of 90

Marks: +1, -0

Let the line of the shortest distance between the lines
L1:

→

)+λ(

−

) and
L2:

→

=(4

)+µ(

−

)
intersect L1 and L2 at P and Q respectively. If (α,β,γ) is the midpoint of the line segment PQ, then 2(α+β+γ) is equal to____

[1-Feb-2024 Shift 1]

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