If the direction cosines of two lines gi...

If the direction cosines of two lines given by the equations `p m+qn+rl=0 and lm+mn+nl=0`, prove that the lines are parallel if `p^2+q^2+r^2=2(pq+qr+rp)` and perpendicular if `pq+qr+rp=0`

Similar Questions

Explore conceptually related problems

The direction cosines of two lines are given by the equations 3m+n+5l=0, 6nl-2lm+5mn=0. find the angle between them

Find the direction colatines of the lines, connected by the relations: l+m+n=0 and 2lm+2ln-mn=0.

If the direction ratio of two lines are given by 3lm-4ln+mn=0 and l+2m+3n=0 , then the angle between the lines, is

The direction cosines of two lines satisfy 2l+2m-n=0 and lm+mn+nl=0 . The angle between these lines is

Find the direction cosine of given system of relation 1+m+n=0,2lm+2nl-mn=0

Prove that the lines whose direction cosines are given by the equations l+m+n=0 and 3lm-5mn+2nl=0 are mutually perpendicular.

Prove that the lines whose directioncosines are given by the equtions l+m+n=0 and 3lm-5mn+2nl=0 are mutually perpendicular.

Find the direction cosines l + m + n of the two lines which are connected by the relation l+ m + n = 0 and mn – 2nl –2lm = 0.

An angle between the lines whose direction cosines are given by the equations, 1+ 3m + 5n =0 and 5 lm - 2m n + 6 nl =0, is :