jee-main 2025 Q6

jee-main · India · session1_23jan_shift2 Vectors 3D & Lines Shortest Distance Between Two Lines
If the square of the shortest distance between the lines $\frac { x - 2 } { 1 } = \frac { y - 1 } { 2 } = \frac { z + 3 } { - 3 }$ and $\frac { x + 1 } { 2 } = \frac { y + 3 } { 4 } = \frac { z + 5 } { - 5 }$ is $\frac { \mathrm { m } } { \mathrm { n } }$, where $\mathrm { m } , \mathrm { n }$ are coprime numbers, then $\mathrm { m } + \mathrm { n }$ is equal to :
(1) 21
(2) 9
(3) 14
(4) 6
If the square of the shortest distance between the lines $\frac { x - 2 } { 1 } = \frac { y - 1 } { 2 } = \frac { z + 3 } { - 3 }$ and $\frac { x + 1 } { 2 } = \frac { y + 3 } { 4 } = \frac { z + 5 } { - 5 }$ is $\frac { \mathrm { m } } { \mathrm { n } }$, where $\mathrm { m } , \mathrm { n }$ are coprime numbers, then $\mathrm { m } + \mathrm { n }$ is equal to :\\
(1) 21\\
(2) 9\\
(3) 14\\
(4) 6