If two lines L, and L, in space, are definedby `L_1={x=lambda y+(sqrtlambda-1}, z=(sqrtlambda-1)y+sqrtlambda} and L_2={x=sqrtmu y+(1-sqrtmu), z=(1-sqrtmu)y+sqrtmu}` then `L_1` is perpendicular to `L_2` for all non-negative reals `lambda and mu,` such that:

If two lines L, in space,are definedby L_(1)={x=lambda y+(sqrt(lambda)-1},z=(sqrt(lambda)-1)y+sqrt(lambda)} and L_(2)={x=sqrt(mu)y+(1-sqrt(mu)),z=(1-sqrt(mu))y+ then L_(1) is perpendicular to L_(2) for all non-negative reals lambda and mu, such that:

If line L:x/1 = y/2 =z/3 and plane E:x-2y +z=6 , then the line L

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of lambda^2 is

Consider two lines L_1:2x+y=4 and L_2:(2x-y=2) .Find the angle between L1 and L2 .

The intersection of the planes 2x-y-3z=8 and x+2y-4z=14 is the line L .The value of for which the line L is perpendicular to the line through (a,2,2) and (6,1,-1) is

If the lines L_1 and L_2 are tangents to 4x^2-4x-24 y+49=0 and are normals for x^2+y^2=72 , then find the slopes of L_1 and L_2dot