Can someone help me solve the following two questions:
1) Find the distance between the lines: $$ L_1: \frac{x-1}{2} = \frac{y+3}{1} = \frac{z}{-1}$$ and $$\displaystyle L_2 : \frac{x+2}{-2}=\frac{y+5}{3} = \frac{z-1}{-5} $$ I've tried taking an arbitrary point on $L_1$ and build the line passing through it and prependcular to $L_1$ , but couldn't figure out how to do it.
2) Find the equation of the plane passing through $(2,-1,5)$ and perpendicular to the planes $3x-2y+z+7=0$ and $5x-4y+3z+1=0$.
Thanks in advance !