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Tap each statement that is true of a line's equation

Exercise and reference answers

Questions
  1. Items
    1. Text
      b sets the direction
      Matches the category
      Yes
    2. Text
      a is a point on the line
      Matches the category
      Yes
    3. Text
      λ sweeps along the line
      Matches the category
      Yes
    4. Text
      It describes a plane
      Matches the category
      No
    5. Text
      b must be a unit vector
      Matches the category
      No
    Category
    True of r = a + λb
  2. Items
    1. Text
      (x₁, y₁, z₁) lies on the line
      Matches the category
      Yes
    2. Text
      l, m, n are direction cosines
      Matches the category
      Yes
    3. Text
      It needs two points
      Matches the category
      No
    4. Text
      It only works in two dimensions
      Matches the category
      No
    Category
    True of the Cartesian form (x−x₁)/l = (y−y₁)/m = (z−z₁)/n

Explanation

Sorting what the vector form does and does not tell you. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.
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