JEE Main | 2014Trigonometric EquationHard
Question
The angle between the lines whose direction consines satisfy the equations l + m + n = 0 and l2 = m2 + n2 is
Options
A.
B.
C.
D.
Solution
l + m + n = 0
l2 = m2 + n2
Now, (-m - n)2 = m2 + n2
⇒ mn = 0
m = 0 or n = 0
If m = 0
then l = - n
l2 + m2 + n2 = 1
Gives
⇒ n = ±
i.e. (l1, m1, n1)
=
If n = 0
then l = - m
l2 + m2 + n2 = 1
⇒ 2m2 = 1
⇒ m2 =
⇒ m = ±
Let m =
l = -
n = 0
(l2, m2, n2)
=
∴ cos θ =
θ =
l2 = m2 + n2
Now, (-m - n)2 = m2 + n2
⇒ mn = 0
m = 0 or n = 0
If m = 0
then l = - n
l2 + m2 + n2 = 1
Gives
⇒ n = ±
i.e. (l1, m1, n1)
=
If n = 0
then l = - m
l2 + m2 + n2 = 1
⇒ 2m2 = 1
⇒ m2 =
⇒ m = ±
Let m =
l = -
n = 0
(l2, m2, n2)
=
∴ cos θ =
θ =
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