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The direction cosines $(l 1, m 1, n 1) and (l 2, m 2, n 2)$ of two lines are connected by the relations $l + m + n = 0$ and $m n = 2 l (m + n)$ then

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l 1 l 2 + m 1 m 2 + n 1 n 2

can be equal to

− 32

l 1 l 2 + m 1 m 2 + n 1 n 2

is equal to

− 32

l 1 m 1 n 1 + l 2 m 2 n 2

is equal to

− 42 33

(l 1 + l 2) (m 1 + m 2) (n 1 + n 2)

is equal to

536

answer is A.

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Detailed Solution

l = − (m + n) ⇒ m n = − 2 (m + n) 2 ⇒ 2 m 2 + 5 m n + 2 n 2 = 0 ⇒ m = − 2 n; 2 m = − n

∴ D R ′ s are (1, − 2, 1) (1, 1, − 2)

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The direction cosines ( l 1 , m 1 , n 1 ) and ( l 2 , m 2 , n 2 ) of two lines are connected by the relations l+m+n=0 and mn=2l(m+n) then

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The direction cosines $(l 1, m 1, n 1) and (l 2, m 2, n 2)$ of two lines are connected by the relations $l + m + n = 0$ and $m n = 2 l (m + n)$ then