Notifications
Clear all
0
15/01/2022 2:08 pm
Topic starter
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m – n = 0 and mn + nl + lm = 0, is
(1) \(\frac{\pi}{2}\)
(2) π - \(cos^{-1}\Big(\frac{4}{9}\Big)\)
(3) \(cos^{-1}\Big(\frac{8}{9}\Big)\)
(4) \(\frac{\pi}{3}\)
1 Answer
0
15/01/2022 3:27 pm
Correct answer: (1) \(\frac{\pi}{2}\)
Explanation:
n = 2 (ℓ + m)
ℓm + n(ℓ + m) = 0
ℓm + 2(ℓ + m)2 = 0
2ℓ2 + 2m2 + 5mℓ = 0
2\(\Big(\frac{ℓ}{m}\Big)^2\) + 2 + 5\(\Big(\frac{ℓ}{m}\Big)\) = 0
2t2 + 5t + 2 = 0
(t + 2)(2t + 1) = 0
⇒ t = -2; - \(\frac{1}{2}\)
(i) \(\frac{\ell}{m}\) = -2
\(\frac{n}{m}\) = -2
(-2m, m, -2m)
(-2, 1, -2)
(ii) \(\frac{\ell}{m}\) = - \(\frac{1}{2}\)
n = -2ℓ
(ℓ, -2ℓ, -2ℓ)
(1, -2, -2)
cosθ = \(\frac{-2-2+4}{\sqrt 9 - \sqrt 9}\) = 0
⇒ 0 = \(\frac{\pi}{2}\)