taiwan-gsat 2025 Q10

taiwan-gsat · Other · ast__math-a 6 marks Vectors 3D & Lines Shortest Distance Between Two Lines
In coordinate space, a plane intersects the plane $x = 0$ and the plane $z = 0$ at lines $L_{1}$ and $L_{2}$, respectively.
Given that $L_{1}$ and $L_{2}$ are parallel, $L_{1}$ passes through the point $(0, 2, -11)$, and $L_{2}$ passes through the point $(8, 21, 0)$,
the distance between $L_{1}$ and $L_{2}$ is $\sqrt{(10-1)(10-2)(10-3)}$. (Express as a simplified radical)
In coordinate space, a plane intersects the plane $x = 0$ and the plane $z = 0$ at lines $L_{1}$ and $L_{2}$, respectively.

Given that $L_{1}$ and $L_{2}$ are parallel, $L_{1}$ passes through the point $(0, 2, -11)$, and $L_{2}$ passes through the point $(8, 21, 0)$,

the distance between $L_{1}$ and $L_{2}$ is $\sqrt{(10-1)(10-2)(10-3)}$. (Express as a simplified radical)