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The direction cosines l , m and n of two lines are connected by the relations l + m + n = 0 and l m = 0 , then the angle between the lines is

Options

  1. Aπ 3
  2. Bπ 4
  3. Cπ 2
  4. D0

Correct answer

A. π 3

Step-by-step solution

Given, l + m + n = 0 ...(i) and l m = 0 i.e. either m = 0 or l = 0 If l = 0 , then putting in equation (i), we get m = - n ∴ Direction ratios are 0 , - n , n i.e. 0 , - 1 , 1 If m = 0 , then putting in equation (i), we get l = - n ∴ Direction ratios are - n , 0 , n i.e. - 1 , 0 , 1 ∴ cos ⁡ θ = 0 × - 1 + - 1 × 0 + 1 × 1 0 2 + - 1 2 + 1 2 - 1 2 + 0 2 + 1 2 = 1 2 ⇒ θ = π 3

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