Chapter Exam

Chapter-11 Introduction to Three-Dimensional Geometry — Online MCQ Test

Q: In three-dimensional geometry, how many coordinate axes are there?

Answer: B. 3 — In 3D geometry, there are three mutually perpendicular coordinate axes: X-axis, Y-axis, and Z-axis.

Q: The three coordinate planes in 3D geometry are XY-plane, YZ-plane, and _____?

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.

Q: How many octants are formed by the three coordinate planes in 3D space?

Answer: C. 8 — Three mutually perpendicular coordinate planes divide 3D space into 8 octants, similar to how 2D divides into 4 quadrants.

Q: The coordinates of a point in 3D space are written as:

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.

Q: Find the distance between points A(1, 2, 3) and B(4, 5, 6).

Answer: A. √27 — Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[9 + 9 + 9] = √27.

Q: The midpoint of the line segment joining P(2, 3, 4) and Q(8, 7, 10) is:

Answer: A. (5, 5, 7) — Using midpoint formula: [(2+8)/2, (3+7)/2, (4+10)/2] = (5, 5, 7].

Q: The coordinates of a point equidistant from A(1, 2, 3) and B(3, 2, 1) lie on:

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.

Q: 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?

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).

Q: 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?

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.

Q: If vertices of a triangle are A(1, 1, 1), B(1, -1, 1), and C(1, 1, -1), then the triangle is:

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.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-11 Introduction to Three-Dimensional Geometry with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. 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.

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Chapter-11 Introduction to Three-Dimensional Geometry — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-11 Introduction to Three-Dimensional Geometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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.

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].

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.

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).

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.

If vertices of a triangle are A(1, 1, 1), B(1, -1, 1), and C(1, 1, -1), then the triangle is: