Three-Dimensional Geometry

The shortest distance between $L_1$ and $L_2$ is

The distance of the point $(1,1,1)$ from the plane passing through the point $(-1,-2,-1)$ and whose normal is perpendicular to both the lines $L_1$ and $L_2$ is

Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5$.

STATEMENT-1: The parametric equations of the line of intersection of the given planes are $x=3+14t$, $y=1+2t$, $z=15t$.

because

STATEMENT-2: The vector $14\hat i+2\hat j+15\hat k$ is parallel to the line of intersection of given planes.