Are these practice questions for Introduction to Three Dimensional Geometry based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Introduction to Three Dimensional Geometry free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Introduction to Three Dimensional Geometry mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Introduction to Three Dimensional Geometry for full coverage.

How many practice questions are there for Introduction to Three Dimensional Geometry?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Introduction to Three Dimensional Geometry Class 11 Mathematics Practice Questions with Answers

easy

Justify why any point with coordinates

(0, y, z)

must lie on the YZ-plane.

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easy

What are the coordinates of the origin in three-dimensional space?

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easy

Formulate the general condition, using inequalities, for a point

P(x, y, z)

to be located in the VI octant.

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easy

Critique the following statement: 'The octant in which a point lies is determined solely by the signs of its

x

and

y

coordinates.'

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easy

List the signs of the coordinates (x, y, z) for a point located in the third octant (III) and the seventh octant (VII).

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easy

Examine which octant the point

(-4, 1, -7)

lies in.

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easy

Calculate the distance of the point

P(3, -4, 12)

from the origin.

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easy

Name the three coordinate planes in a three-dimensional rectangular coordinate system.

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easy

How many octants do the three coordinate planes divide the space into?

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easy

A point has coordinates

(m+1, m-3, 5)

and it lies in the ZX-plane. Calculate the value of

m

.

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easy

A point lies on the z-axis. What are its x-coordinate and y-coordinate?

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easy

State the formula for the distance between two points

P(x_1, y_1, z_1)

and

Q(x_2, y_2, z_2)

. Also, write the formula for the distance of a point

Q(x, y, z)

from the origin.

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medium

Propose the coordinates of a point in the third octant that is equidistant from the XY-plane and the ZX-plane, and justify your proposal.

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medium

Explain what the coordinates

(x, y, z)

of a point P represent in terms of its perpendicular distances from the three coordinate planes.

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medium

Analyze if the triangle formed by the points

A(3, 5, -4)

,

B(-1, 1, 2)

, and

C(-5, -5, -2)

is an isosceles triangle.

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medium

The points

A(1, 2, 3)

,

B(-1, -2, -1)

, and

C(2, 3, 2)

are three consecutive vertices of a parallelogram. Evaluate the coordinates of the fourth vertex, D.

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medium

Derive the coordinates of the point on the y-axis which is equidistant from the points

P(3, 1, 2)

and

Q(-2, 5, 4)

.

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medium

Demonstrate that the points

A(1, 1, 1)

,

B(-2, 4, 1)

, and

C(-1, 5, 5)

form a right-angled triangle.

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medium

Justify conclusively whether the points

A(1, -1, 3)

,

B(2, -4, 5)

, and

C(5, -13, 11)

are collinear or form the vertices of a triangle.

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medium

Evaluate whether three distinct points A, B, and C can form a triangle if the distance

AB + BC

is exactly equal to the distance

AC

. Justify your reasoning.

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medium

Describe the step-by-step process to locate a point

P(a, b, c)

in space, where

a, b, c

are all positive real numbers. Start from the origin O.

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medium

Identify the plane determined by the y-axis and the z-axis taken together.

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medium

Formulate and prove a theorem stating the relationship between the length of the main diagonal of a rectangular parallelopiped and the lengths of its three distinct edges meeting at a vertex.

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medium

Calculate the coordinates of a point on the y-axis which is at a distance of

\sqrt{13}

units from the point

P(2, -3, 0)

.

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medium

Summarize the key components of a rectangular coordinate system in three dimensions. Include a description of the coordinate axes, coordinate planes, and the origin.

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medium

Explain the sign convention for distances measured along the axes from the origin.

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medium

Formulate an equation that represents the set of all points

P(x, y, z)

such that the sum of its perpendicular distances from the XY-plane and the YZ-plane is equal to its perpendicular distance from the ZX-plane.

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medium

Find the coordinates of the point that divides the line segment joining the points

P(-2, 3, 5)

and

Q(1, -4, 6)

in the ratio

2:3

(i) internally and (ii) externally.

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medium

Calculate the ratio in which the YZ-plane divides the line segment formed by joining the points

(-2, 4, 7)

and

(3, -5, 8)

.

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medium

The centroid of a triangle

PQR

is at the origin

(0, 0, 0)

. If the coordinates of

P

and

Q

are

(4, -2, 5)

and

(-3, 1, 2)

respectively, calculate the coordinates of vertex

R

.

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medium

Find the coordinates of the point that is the reflection of

(-5, 2, -8)

in the YZ-plane.

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medium

Calculate the coordinates of a point on the z-axis that is equidistant from the points

P(1, 5, 7)

and

Q(5, 1, -4)

.

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medium

Identify the octants in which the following points lie: (a)

(2, -4, 6)

(b)

(-1, -2, 3)

(c)

(5, -3, -1)

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medium

Describe the general form of the coordinates for any point lying in the YZ-plane. Explain why the x-coordinate is zero.

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hard

Demonstrate that the points

A(1, 0, 1)

,

B(2, 2, 0)

,

C(3, 0, -1)

, and

D(2, -2, 0)

are the vertices of a rhombus. Analyze if this rhombus is also a square.

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hard

Critique the method of using only the distance formula to prove that four given points form a square. What additional verification is necessary and why?

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hard

Derive the formula for the coordinates of the circumcenter of a right-angled triangle whose vertices are

A(a, 0, 0)

,

B(0, b, 0)

, and

C(0, 0, c)

. Justify your reasoning.

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hard

A point P moves such that its distance from point

A(2, 0, 0)

is always twice its distance from point

B(-1, 0, 0)

. Derive the equation of the locus of P and identify the geometric shape it represents. Justify your conclusion.

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hard

Find the equation of the set of points

P(x, y, z)

such that the sum of the squares of its distances from the points

A(1, 1, 1)

and

B(-1, -1, -1)

is equal to 18. Analyze the geometric shape this equation represents.

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hard

Explain the concept of octants in three-dimensional geometry. List the names of all eight octants and present the signs of the coordinates (x, y, z) for each octant in a table format.

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hard

Recall the coordinates of a point on the y-axis at a distance of 7 units from the origin in the negative direction.

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hard

Design a set of coordinates for three distinct points A, B, and C that form an isosceles right-angled triangle with the right angle at vertex B. Justify your design using the distance formula.

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hard

A point

P(x, y, z)

is such that its distance from the point

A(2, 0, 0)

is twice its distance from the point

B(-1, 0, 0)

. Solve for the equation of the set of all such points

P

.

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hard

Three consecutive vertices of a parallelogram are

A(1, 2, -1)

,

B(3, 6, 11)

, and

C(5, 1, 0)

. Calculate the coordinates of the fourth vertex

D

.

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hard

Design a problem to demonstrate that four given points form a rhombus but not a square. Create the coordinates for the four vertices, and then provide a complete justification by calculating side lengths and diagonal lengths, explaining why the properties of a rhombus are met but those of a square are not.

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Introduction to Three Dimensional GeometryClass 11 Mathematics Practice Questions