Question

The direction cosines of two lines are related by l + m + n = 0 and al2 + bm2 + cn2 = 0. The lines are parallel if –

• A. a + b + c = 0
• B. a–1 + b–1 + c–1 = 0
• C. a = b = c
• D. None of these

Answer 1

Answer: (B)

a–1 + b–1 + c–1 = 0

Answer 2

For n = – (l + m), the second relation gives

al2 + bm2 + c(l + m)2 = 0

or (a + c) l2 + 2clm + (b + c) m2 = 0.

For parallel lines, the two roots must be equal

̃ 4c2 – 4(b + c) (a + c) = 0

̃ ab + bc + ca = 0