If the lines `L_(1):(x-1)/(3)=(y-lambda)/(1)=(z-3)/(2)` and `L_(2):(x-3)/(1)=(y-1)/(2)=(z-2)/(3)` are coplanar, then the equation of the plane passing through the point of intersection of `L_(1)&L_(2)` which is at a maximum distance from the origin is

The shortest distance between lines L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2) , L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) is

Consider the lines L_(1):(x-1)/(2)=(y)/(-1)=(z+3)/(1),L_(2):(x-4)/(1)=(y+3)/(1)=(z+3)/(2) and the planes P_(1):7x+y+2z=3," "P_(2):3x+5y-6z=4. Let ax+by+cz=d the equation of the plane passing through the point of intersection of lines L_(1) and L_(2) and perpendicualr to planes P_(1) and P_(2) . Match List I with List II and select the correct answer using the code given below the lists.

The equation of a plane passing through the line of intersection of the planes x+2y+3z=2 and x-y+z=3 and at a distance (2)/(sqrt(3)) from the point (3,1,-1) is

Consider the lines L_(1): (x-1)/(2)=(y)/(-1)= (z+3)/(1) , L_(2): (x-4)/(1)= (y+3)/(1)= (z+3)/(2) and the planes P_(1)= 7x+y+2z=3, P_(2): 3x+5y-6z=4 . Let ax+by+cz=d be the equation of the plane passing through the point of intersection of lines L_(1) and L_(2) , and perpendicular to planes P_(1) and P_(2) . Match Column I with Column II.

Consider the line L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) The shortest distance between L_(1) and L_(2) is

Consider the line L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) The shortest distance between L_(1) and L_(2) is

Two lines L_(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L_(2) : x=alpha, (y)/(-1)=(z)/(2-alpha) are coplanar. Then, alpha can take value(s)