Question

find the angle between lines whose direction cosine satisfy the equation l+m+n=0 and Lsquare+msquare-nsquare=0​

Answer 1

Answer:

Given that direction cosines of two lines satisfy the equations l+m+n=0 and l2=m2+n2

Eliminating l, we get

(m+n)2=m2+n2

∴2mn=0 ⇒m=0 or n=0

When m=0, then l+n=0 or l=−n

∴1l=0m=−1n

When n=0, then l+m=0 or l=−m

∴1l=−1m=0n

Hence, the direction ratios of the lines are (1,0,−1),(1,−1,0)

cosθ=2⋅21+0+0=21

Therefore, angle between the lines is 3