Given

l + 3m + 5n = 0

and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0

From eq. (1) we have

$$l$$ = $$-$$ 3m $$-$$ 5n

Put the value of $$l$$ in eq. (2), we get ;

5 ($$-$$3m $$-$$5n) m $$-$$ 2mn + 6n ($$-$$ 3m $$-$$ 5n) = 0

$$ \Rightarrow $$  15m² + 45mn + 30n² = 0

$$ \Rightarrow $$ m² + 3mn + 2n² = 0

$$ \Rightarrow $$  m² + 2mn + mn + 2n² = 0

$$ \Rightarrow $$ $$\,\,\,$$ (m + n) (m + 2n) = 0

$$ \therefore $$  m = $$-$$ n   or   m = $$-$$ 2n

For m = $$-n, $$ $$l$$ = $$-$$ 2n

And for m = $$-$$ 2n, $$l$$ = n

$$ \therefore $$   ($$l$$, m, n) = ($$-$$2n, $$-$$n, n) Or ($$l$$, m, n) = (n, $$-$$ 2n, n)

$$ \Rightarrow $$  ($$l$$, m, n) = ($$-$$2, $$-$$1, 1) Or ($$l$$, m, n) = (1, $$-$$ 2, 1)

Therefore, angle between the lines is given as :

cos ($$\theta $$) = $${{\left( { - 2} \right)\left( 1 \right) + \left( { - 1} \right).\left( { - 2} \right) + \left( 1 \right)\left( 1 \right)} \over {\sqrt 6 .\sqrt 6 }}$$

$$ \Rightarrow $$ cos ($$\theta $$) = $${1 \over 6}$$ $$ \Rightarrow $$  $$\theta $$ =cos^$$-$$1 $$\left( {{1 \over 6}} \right)$$