Question

find the direction cosines of the two lines which are connected by the relation l+m+n=0 and 2 mn+3nl-5lm=0​

Answer 1

Answer:

Step-by-step explanation:

he dc's of two lines are connected by ;

l + m + n = 0 ···· ···· ····(1) &

2mn + 3nl - 5lm = 0 ····· ··· ··(2) . To find them, eliminate say l from these two eqns., we get,

2mn - 3n(m + n) + 5m(m + n) = 0 ==>

5 (m/n)^2 + 4 (m/n) - 3 = 0 . A quadratic in (m/n) therefore, if (m/n) & (m'/n') be its roots then ;

(m/n) · (m'/n') = - 3/5 or (m m'/3) =(nn'/-5) ··· (3). Similarly eliminating n between (1) & (2) , we get, 3(l/m)^2 + 10 (l/m) + 2 = 0 and it implies ;

(l/m) · (l'/m') = 2/3 or (l l'/2) = (m m'/3) ··· ··· ·· (4). From (3) & (4), we get,

(l l'/2) = (m m'/3) = (n n'/-5) . Now these eqns. Implies that ;

l l' + m m' + n n' = 2 + 3 - 5 = 0 . Hence the given lines are perpendicular to each other .