Three Dimensional Geometry MCQ

Test your knowledge with important Three Dimensional Geometry MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Three Dimensional Geometry MCQs at Bissoy

• Find k for the given plane x + 2y + kz + 2 = 0 and directional ratios of a line (8, 3, 2), if they are parallel to each other.
  ক

  21

  খ

  -17

  গ

  12

  ঘ

  -7
• The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.
  ক

  4

  খ

  -14

  গ

  6

  ঘ

  -8
• The condition a1a + b1b + c1c = 0 is for a plane and a line are _____ to each other.
  ক

  integral

  খ

  parallel

  গ

  perpendicular

  ঘ

  concentric
• What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?
  ক

  a1a2 . b1b2 . c1c2 = 0

  খ

  a1a + b1b + c1c = 0

  গ

  a1a2 + b1b2 – c1c2 = 0

  ঘ

  a1a2 + b1b2 – c1c2 = 0
• Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
  ক

  21

  খ

  17

  গ

  12

  ঘ

  11
• The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
  ক

  4

  খ

  2

  গ

  6

  ঘ

  8
• The condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other.
  ক

  integral

  খ

  parallel

  গ

  perpendicular

  ঘ

  concentric
• _____ planes have an angle 90 degrees between them.
  ক

  Orthogonal

  খ

  Tangential

  গ

  Normal

  ঘ

  Parallel
• What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other?
  ক

  a1a2 . b1b2 . c1c2 = 0

  খ

  a1a2 + b1b2 + c1c2 = 0

  গ

  a1a2 + b1b2 – c1c2 = 0

  ঘ

  a1a2 + b1b2 – c1c2 = 0
• Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
  ক

  21

  খ

  – 7

  গ

  12

  ঘ

  – 8
• Which trigonometric function is used to find the angle between two planes?
  ক

  Tangent

  খ

  Cosecant

  গ

  Secant

  ঘ

  Sine
• _____ is the angle between the normals to two planes.
  ক

  Normal between the planes

  খ

  The angle between the planes

  গ

  Tangent between the planes

  ঘ

  Distance between the planes
• If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then what is the angle between the two lines?
  ক

  cot⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

  খ

  sin⁡θ=\(\left |l_1 \,l_2+m_1 \,n_2+n_1 \,m_2\right |\)

  গ

  tan⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

  ঘ

  cos⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)
• The direction ratios of the line segment joining \(P(x_1,y_1,z_1)\) and \(Q(x_2,y_2,z_2)\) is given by _______, ____________ and __________
  ক

  \(x_2+x_1,y_2+y_1,z_2+z_1\)

  খ

  \(x_2-x_1,y_2+y_1,z_2-z_1\)

  গ

  \(x_2-x_1,y_2-y_1,z_2-z_1\)

  ঘ

  \(x_2+x_1,y_2-y_1,z_2+z_1\)
• If coordinates of vertices of a triangle are (7, 6, 4), (5, 4, 6), (9, 5, 8), find the coordinates of centroid of the triangle.
  ক

  (7, 5, 3)

  খ

  (7, 3, 5)

  গ

  (5, 3, 7)

  ঘ

  (3, 5, 7)
• Find midpoint of (1, 4, 6) and (5, 8, 10).
  ক

  (6, 12, 8)

  খ

  (3, 6, 8)

  গ

  (1, 9, 12)

  ঘ

  (4, 9, 12)
• In which octant does the point (-1, 5, -7) lies?
  ক

  1st

  খ

  2nd

  গ

  6th

  ঘ

  7th
• In which octant does the point (-1, 5, 7) lies?
  ক

  1st

  খ

  2nd

  গ

  6th

  ঘ

  7th
• In which octant does the point (-1, – 5, -7) lies?
  ক

  1st

  খ

  2nd

  গ

  6th

  ঘ

  7th
• In which octant does the point (1, 5, 7) lies?
  ক

  1st

  খ

  2nd

  গ

  6th

  ঘ

  7th
• 3-D geometry has ______________ octants.
  ক

  1

  খ

  2

  গ

  4

  ঘ

  8
• 2-D geometry has ______________ quadrants.
  ক

  1

  খ

  2

  গ

  4

  ঘ

  8
• Find the distance of point (2, 3, 5) from X-Z plane.
  ক

  2 units

  খ

  3 units

  গ

  5 units

  ঘ

  1 unit
• Find the distance of point (2, 3, 5) from Y-Z plane.
  ক

  2 units

  খ

  3 units

  গ

  5 units

  ঘ

  1 unit
• Find the distance of point (2, 3, 5) from X-Y plane.
  ক

  2 units

  খ

  3 units

  গ

  5 units

  ঘ

  1 unit
• The point (3, 0, 4) lie on _________
  ক

  X-Y plane

  খ

  Y-Z plane

  গ

  X-Z plane

  ঘ

  X-axis
• The point (4, 2, 0) lie on _________
  ক

  X-Y plane

  খ

  Y-Z plane

  গ

  X-Z plane

  ঘ

  X-axis
• The point (0, 2, 4) lie on _________
  ক

  X-Y plane

  খ

  Y-Z plane

  গ

  X-Z plane

  ঘ

  X-axis
• The point (0, 2, 0) lie on _________
  ক

  X-axis

  খ

  Y-axis

  গ

  Z-axis

  ঘ

  X-Y plane
• The point (0, 0, 3) lie on ____________
  ক

  X-axis

  খ

  Y-axis

  গ

  Z-axis

  ঘ

  X-Y plane