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      Question

      Let a line pass through the origin and make equal angles

      with the coordinate axes. Then the direction cosines of the line are:
      A (1/√2, 1/√2, 0) Correct Answer Incorrect Answer
      B (1/√3, 1/√3, 1/√3) Correct Answer Incorrect Answer
      C (1/2, 1/2, 1/2) Correct Answer Incorrect Answer
      D (1/√6, 1/√3, 1/2) Correct Answer Incorrect Answer

      Solution

      Let the direction cosines be l, m, n.
      If the line makes equal angles with the coordinate axes, then: l = m = n And we know the identity for direction cosines:
      l² + m² + n² = 1 Substitute l = m = n: ⇒ 3l² = 1
      ⇒ l² = 1/3
      ⇒ l = m = n = 1/√3 So, the direction cosines are (1/√3, 1/√3, 1/√3)

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