Three Dimensional Geometry Test! Trivia Quiz

15 Questions | Total Attempts: 205

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Three Dimensional Geometry Test! Trivia Quiz

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Questions and Answers
  • 1. 
    Find the length of the perpendicular drawn from the origin to the plane 2x-3y + 6z + 21 = 0.
    • A. 

      3

    • B. 

      4

    • C. 

      5

    • D. 

      6

  • 2. 
    Write the direction cosines of the vector -2i + j – 5k
    • A. 
    • B. 
    • C. 
    • D. 
  • 3. 
    If a line makes angles 900, 1350, 450 with x, y, and z-axes respectively, find its direction cosines.
    • A. 
    • B. 
    • C. 
    • D. 
  • 4. 
    There are two lines in which one line is passing through the points (4, 7, 8) (2, 3, 4) & another line is passing through the points (-1, -2, 1), (1, 2, 5). What is true regarding these lines?
    • A. 

      AB is parallel to CD

    • B. 

      AB is perpendicular to CD

    • C. 

      AB is inclined to CD at certain angle

    • D. 

      None of these

  • 5. 
    Find the angle between the following pair of lines:
    • A. 
    • B. 
    • C. 
    • D. 
  • 6. 
    Find the Cartesian equation of the line which passes through the point (-2, 4, -5) and is parallel to the line:
    • A. 
    • B. 
    • C. 
    • D. 
  • 7. 
    Find the coordinates of the point, where the line  intersects the plane x – y + z – 5 = 0. Also find the angle between the line & the plane.
    • A. 
    • B. 
    • C. 
    • D. 
  • 8. 
    Find the vector equation of the plane which contains the line of intersection of the planes & which is perpendicular to the plane
    • A. 
    • B. 
    • C. 
    • D. 
  • 9. 
    Find the coordinates of the point where the line through (3, -4, -5) and (2, -3, 1) crosses the plane, passing through the points (2, 2, 1), (3, 0, 1) and (4, -1, 0).
    • A. 

      (1, -2, 7)

    • B. 

      (1, 2, 7)

    • C. 

      (1, -2, 5)

    • D. 

      (2, -2, 7)

  • 10. 
    Show that the lines are intersecting. Hence find their point of intersection.
    • A. 

      (-1, -6, 12)

    • B. 

      (-1, 6, -12)

    • C. 

      (1, -6, -12)

    • D. 

      (-1, -6, -12)

  • 11. 
    Find the vector equation of the plane through the points (2, 1,-1) and (-1, 3, 4) and perpendicular to the plane x -2y+ 4z = 10.
    • A. 
    • B. 
    • C. 
    • D. 
  • 12. 
    Find the equation of the plane passing through the line of intersection of the planes whose perpendicular distance from origin is unity.
    • A. 
    • B. 
    • C. 
    • D. 
  • 13. 
    Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0
    • A. 

      X - z - 2 = 0

    • B. 

      X -y + 2 = 0

    • C. 

      X - z + 2 = 0

    • D. 

      Y - z + 2 = 0

  • 14. 
    Find the Cartesian equation of the plane which contains the line of intersection of the planes
    • A. 

      33x +45y + 50z - 41 = 0

    • B. 

      33x + 45y + 50z - 41 = 0

    • C. 

      X + 45y + 50z - 41 = 0

    • D. 

      33x + y + 50z - 41 = 0

  • 15. 
    Find the shortest distance between the lines:
    • A. 
    • B. 
    • C. 
    • D.