jee-main 2025 Q13

jee-main · India · session1_29jan_shift1 Vectors 3D & Lines Shortest Distance Between Two Lines
Let $\mathrm{L}_1: \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{2}$ and $\mathrm{L}_2: \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z}{1}$ be two lines. Let $L_3$ be a line passing through the point $(\alpha, \beta, \gamma)$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $\mathrm{L}_1$, then $|5\alpha - 11\beta - 8\gamma|$ equals:
(1) 20
(2) 18
(3) 25
(4) 16
Let $\mathrm{L}_1: \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{2}$ and $\mathrm{L}_2: \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z}{1}$ be two lines. Let $L_3$ be a line passing through the point $(\alpha, \beta, \gamma)$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $\mathrm{L}_1$, then $|5\alpha - 11\beta - 8\gamma|$ equals:\\
(1) 20\\
(2) 18\\
(3) 25\\
(4) 16