Find the direction cosines , m, n of line which are connected by the relations + m + n = 0, 2mn + 2m – n = 0.
Text Solution
Verified by ExpertsD
or ;k 
Sol. n = – ( + m) ........(1) 2mn + 2ml – nl = 0 ............(2)
– 2k ( + m) + 2m + ( + m) = 0
⇒ – 2m – 2m 2 + 2m + 2 + m = 0 ⇒ 2 + m – 2m 2 = 0 ⇒ 
Case - I :
We have 
⇒ = m So , n = – 2 So , : m : n = 1 : 1 : – 2.
⇒ direction cosines are ,¡ 
or 
Case - II :
We have ; 
⇒ = – 2m ⇒ : m : n = – 2 : 1 : 1
hence direction cosines are , 
or ; 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems