Three-dimension...

Two lines whose direction ratios are a₁ , b₁ , c₁  and a₂ , b₂ , c₂  are parallel, if

For which value of a lines    and   are perpendicular?

The shortest distance between the lines whose equations are    and   is:

Two lines whose direction ratios are a₁ ,b₁ ,c₁  and a₂ ,b₂ ,c₂  are perpendicular, if

The shortest distance between the parallel lines whose equations are   and  

The angle between the pair of lines given by and   is:

The angle between the lines x = 2y = –3z and –4x = 6y = –z is:​

The angle between the lines whose direction cosines are given by the equations  3l + m + 5n = 0, 6nm - 2nl + 5lm = 0  is:

The angle between the lines    and   is:

The length of the shortest distance between the lines    and   is: