The angle between the lines whose direction cosines satisfy the equations ℓ + m + n = 0 and ℓ2 = m2 + n2 is

Engineering

Mathematics

Direction Cosines and Direction Ratio

Question

The angle between the lines whose direction cosines satisfy the equations ℓ + m + n = 0 and ℓ² = m² + n² is

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

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ℓ = –m – n

(m + n)² = m² + n² ⇒ 2mn = 0

m = 0, ℓ = –n

n = 0, ℓ = m

Dr's are : –n, 0, n and –m, m, 0

or : –1, 0, 1 and –1, 1, 0

$\cos θ = \frac{1}{\sqrt{2} . \sqrt{2}} \Rightarrow θ = \frac{π}{3}$