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Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions
  1. Question
    Three of these statements about direction ratios are false.
    Choices
    1. Item
      They are proportional to direction cosines
      Correct
      Yes
    2. Explanation
      That is true of direction COSINES, not ratios.
      Item
      They satisfy a² + b² + c² = 1
    3. Explanation
      Any proportional triple works, so there are infinitely many.
      Item
      A line has only one set of them
    4. Explanation
      They are plain numbers, not angles.
      Item
      They are always angles
  2. Question
    Three of these statements about skew lines are false.
    Choices
    1. Item
      They lie in different planes
      Correct
      Yes
    2. Explanation
      Skew lines never intersect.
      Item
      They intersect at one point
    3. Explanation
      Skew rules out parallel as well.
      Item
      They are parallel
    4. Explanation
      Two coplanar lines must either meet or be parallel.
      Item
      They lie in the same plane

Explanation

Each trap is a real one: normalising the wrong triple, or forgetting that skew lines cannot be coplanar. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.
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