Three Dimensional Geometry Test! Trivia Quiz

15 Questions | By Jagranjosh | Updated: Mar 22, 2022 | Attempts: 485

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Three Dimensional Geometry Test! Trivia Quiz - Quiz

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.

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.
4.

If a line makes angles 90⁰, 135⁰, 45⁰ with x, y, and z-axes respectively, find its direction cosines.
- A.
- B.
- C.
- D.
5.

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.
6.

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
7.

Find the angle between the following pair of lines:
- A.
- B.
- C.
- D.
8.

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.
9.

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
10.

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)
11.

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
12.

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)
13.

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.
14.

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

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.