Chapter-11 Introduction to Three-Dimensional Geometry — Online MCQ Test
MATHS · Grade 11 · CBSE(NCERT)
Practice Chapter-11 Introduction to Three-Dimensional Geometry with a free chapter-wise online MCQ test.
This chapter covers: Coordinate axes - Coordinate planes - Octants - Coordinates of a point in space - Distance formula - Section formula.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-11 Introduction to Three-Dimensional Geometry — Important Questions & Answers
In three-dimensional geometry, how many coordinate axes are there?
- A. 2
- B. 3
- C. 4
- D. 5
Answer: B. 3
In 3D geometry, there are three mutually perpendicular coordinate axes: X-axis, Y-axis, and Z-axis.
In 3D geometry, there are three mutually perpendicular coordinate axes: X-axis, Y-axis, and Z-axis.
The three coordinate planes in 3D geometry are XY-plane, YZ-plane, and _____?
- A. XZ-plane
- B. ZX-plane
- C. Both A and B
- D. None of these
Answer: C. Both A and B
The three coordinate planes are XY-plane, YZ-plane, and ZX-plane (or XZ-plane), which are the same plane with different notations.
The three coordinate planes are XY-plane, YZ-plane, and ZX-plane (or XZ-plane), which are the same plane with different notations.
How many octants are formed by the three coordinate planes in 3D space?
- A. 4
- B. 6
- C. 8
- D. 12
Answer: C. 8
Three mutually perpendicular coordinate planes divide 3D space into 8 octants, similar to how 2D divides into 4 quadrants.
Three mutually perpendicular coordinate planes divide 3D space into 8 octants, similar to how 2D divides into 4 quadrants.
The coordinates of a point in 3D space are written as:
- A. (x, y)
- B. (x, y, z)
- C. (x, y, z, w)
- D. (y, z)
Answer: B. (x, y, z)
A point in three-dimensional space is represented by an ordered triplet (x, y, z) where x, y, z are the distances along X, Y, and Z axes respectively.
A point in three-dimensional space is represented by an ordered triplet (x, y, z) where x, y, z are the distances along X, Y, and Z axes respectively.
Find the distance between points A(1, 2, 3) and B(4, 5, 6).
- A. √27
- B. √36
- C. 9
- D. 6
Answer: A. √27
Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[9 + 9 + 9] = √27.
Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[9 + 9 + 9] = √27.
The midpoint of the line segment joining P(2, 3, 4) and Q(8, 7, 10) is:
- A. (5, 5, 7)
- B. (10, 10, 14)
- C. (3, 2, 3)
- D. (6, 5, 7)
Answer: A. (5, 5, 7)
Using midpoint formula: [(2+8)/2, (3+7)/2, (4+10)/2] = (5, 5, 7].
Using midpoint formula: [(2+8)/2, (3+7)/2, (4+10)/2] = (5, 5, 7].
The coordinates of a point equidistant from A(1, 2, 3) and B(3, 2, 1) lie on:
- A. A circle
- B. A line perpendicular to AB
- C. The perpendicular bisector plane of AB
- D. A sphere
Answer: C. The perpendicular bisector plane of AB
Points equidistant from two given points lie on the perpendicular bisector plane of the line segment joining them.
Points equidistant from two given points lie on the perpendicular bisector plane of the line segment joining them.
Three vertices of a rectangle are A(0, 0, 0), B(2, 0, 0), and C(2, 3, 0). What are the coordinates of the fourth vertex D?
- A. (0, 3, 0)
- B. (0, 0, 3)
- C. (3, 2, 0)
- D. (2, 2, 0)
Answer: A. (0, 3, 0)
For a rectangle ABCD, the fourth vertex D must satisfy that DC is parallel to AB and AD is parallel to BC. Thus D = (0, 3, 0).
For a rectangle ABCD, the fourth vertex D must satisfy that DC is parallel to AB and AD is parallel to BC. Thus D = (0, 3, 0).
A point P(x, y, z) is at distance 13 from the origin and also from the point (2, 3, 6). Which equation satisfies this condition?
- A. 2x + 3y + 6z = 49
- B. 4x + 6y + 12z = 49
- C. x + y + z = 13
- D. x² + y² + z² = 169
Answer: A. 2x + 3y + 6z = 49
Setting PA = PB where A is origin and B(2,3,6): x² + y² + z² = (x-2)² + (y-3)² + (z-6)² simplifies to 2x + 3y + 6z = 49.
Setting PA = PB where A is origin and B(2,3,6): x² + y² + z² = (x-2)² + (y-3)² + (z-6)² simplifies to 2x + 3y + 6z = 49.
If vertices of a triangle are A(1, 1, 1), B(1, -1, 1), and C(1, 1, -1), then the triangle is:
- A. Equilateral with side 2√2
- B. Isosceles right-angled with legs 2
- C. Right-angled at A with sides 2, 2, 2√2
- D. Equilateral with side 2
Answer: C. Right-angled at A with sides 2, 2, 2√2
AB = 2, AC = 2, BC = 2√2. AB² + AC² = 4 + 4 = 8 = BC², confirming right angle at A.
AB = 2, AC = 2, BC = 2√2. AB² + AC² = 4 + 4 = 8 = BC², confirming right angle at A.