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BITSAT2019MathematicsThree Dimensional GeometryActual

The angle between the lines whose direction cosine satisfy the equations l + m + n = 0 and l 2 = m 2 + n 2 is

Options

  1. Aπ 3
  2. Bπ 4
  3. Cπ 6
  4. Dπ 2

Correct answer

A. π 3

Step-by-step solution

We have, l + m + n = 0 . . . ( i ) and l 2 = m 2 + n 2 . . . ( ii ) Putting the value of l in Eq. ( ii ) , we get ( m + n ) 2 = m 2 + n 2 ⇒   m 2 + n 2 + 2 m n = m 2 + n 2 ⇒   m n = 0 ⇒   m = 0 , n = 0 when m = 0 , l = - n ∴ Direction cosines are - 1 2 , 0 , 1 2 . When n = 0 , l = - m ∴ Direction cosines are - 1 2 , 1 2 , 0 . Angle between lines are cos θ = - 1 2 × - 1 2 + 0 × 1 2 + 1 2 × 0 cos θ = 1 2 , θ = π / 3

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