xyz

Chapter 11 · Class XI Mathematics · MCQ Practice

MCQ Practice Arena

Introduction to 3D Geometry

Step Into Space — Build the Foundation for Vectors & 3D in Class XII

📋 50 MCQs ⭐ 0 PYQs ⏱ 70 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

18Easy

20Medium

12Hard

0PYQs

70 secAvg Time/Q

6Topics

Easy 36% Medium 40% Hard 24%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSAT

Introduction to 3D Geometry MCQs are direct, formula-based, and fast to solve — high scoring for the effort invested. JEE Main asks 2–3 questions on distance and section formula in 3D. CBSE includes centroid and midpoint MCQs. This chapter is the launchpad for 3D Vectors in Class XII which carries 10+ marks in JEE.

Topic-wise MCQ Breakdown

Coordinate Axes & Planes16 Q

Octants & Sign Convention6 Q

Distance Formula (3D)12 Q

Distance from Planes/Axes10 Q

Special Locus Conditions4 Q

Symmetry & Reflection2 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$d=√[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]$

$Section: P=((mx₂+nx₁)/(m+n), ...)$

$Midpoint: ((x₁+x₂)/2,(y₁+y₂)/2,(z₁+z₂)/2)$

$Centroid: ((x₁+x₂+x₃)/3,...)$

MCQ Solving Strategy

All 2D formulas extend to 3D by adding the z-term — internalise this pattern and the chapter becomes trivial. For octant MCQs, memorise the sign convention: (+,+,+) is the 1st octant. Section formula MCQs: check whether the division is internal or external before substituting. Collinearity: check if one vector is a scalar multiple of another.

⚠ Common Traps & Errors

⚠Distance from XY-plane is |z|, not √(x²+y²)
⚠External division: use − sign in section formula
⚠Centroid uses all 3 vertices — not midpoint formula
⚠Octant signs: (−,+,+) is 2nd octant not 6th

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Distance between two points, midpoint, identify octant

② Medium

Section formula, centroid, collinearity check

③ Hard

Combined 3D problems, distance from axes/planes

★ PYQ

JEE Main — distance + section formula; CBSE — centroid MCQs

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Limits & Derivatives MCQs

🎯 Knowledge Check

Maths — INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

50 Questions Class 11 MCQs

What is the ordered triplet representing the coordinates of a point in three-dimensional space?
(Easy | NCERT)

a a. $(x, y)$ b b. $(x, y, z)$ c c. $(x, z)$ d d. $(y, z)$

Which axis is perpendicular to both the $x$-axis and the $y$-axis?
(Easy | NCERT)

a a. $x$-axis b b. $y$-axis c c. $z$-axis d d. Origin

The coordinates of the origin are:
(Easy | NCERT)

a a. $(1,1,1)$ b b. $(0,0)$ c c. $(0,0,0)$ d d. $(1,0,0)$

A point lies on the $x$-axis if:
(Easy | NCERT)

a a. $y=0, z=0$ b b. $x=0, z=0$ c c. $x=0, y=0$ d d. $x=y=z$

The point $(3,4,0)$ lies in:
(Easy | NCERT)

a a. $xy$-plane b b. $yz$-plane c c. $zx$-plane d d. none

Distance of $(a,b,c)$ from the $xy$-plane is:
(Easy | NCERT)

a a. $|a|$ b b. $|b|$ c c. $|c|$ d d. $\sqrt{a^2+b^2+c^2}$

Which point lies in the $yz$-plane?
(Easy | NCERT)

a a. $(0,2,3)$ b b. $(1,0,2)$ c c. $(2,3,0)$ d d. $(1,1,1)$

Coordinates of a point on the $z$-axis are:
(Easy | NCERT)

a a. $(x,0,0)$ b b. $(0,y,0)$ c c. $(0,0,z)$ d d. $(x,y,0)$

Number of coordinate planes in three-dimensional geometry is:
(Easy | NCERT)

a a. 1 b b. 2 c c. 3 d d. 4

The plane containing the $x$- and $z$-axes is:
(Easy | NCERT)

a a. $xy$-plane b b. $yz$-plane c c. $zx$-plane d d. vertical plane

Distance of $(0,-3,5)$ from the $z$-axis is:
(Medium | NCERT)

a a. 0 b b. 3 c c. 5 d d. $\sqrt{34}$

A point equally distant from all coordinate planes is:
(Medium | NCERT)

a a. $(1,2,3)$ b b. $(2,2,2)$ c c. $(3,2,1)$ d d. $(1,1,2)$

Distance between $(0,0,0)$ and $(1,2,2)$ is:
(Medium | NCERT)

a a. 3 b b. $\sqrt{9}$ c c. $\sqrt{8}$ d d. $\sqrt{5}$

If the distance of a point from the $x$-axis is zero, then:
(Medium | NCERT)

a a. $x=0$ b b. $y=0$ c c. $z=0$ d d. $y=z=0$

Distance of $(2,-3,6)$ from the $xz$-plane is:
(Medium | NCERT)

a a. 2 b b. 3 c c. 6 d d. 7

Which coordinates remain unchanged when a point moves parallel to the $x$-axis?
(Medium | NCERT)

a a. $x$ b b. $y$ c c. $z$ d d. $y$ and $z$

Locus of points with $x=0$ is:
(Medium | NCERT)

a a. $xy$-plane b b. $yz$-plane c c. $zx$-plane d d. $x$-axis

Distance of a point from the origin equals:
(Medium | NCERT)

a a. abscissa b b. ordinate c c. applicate d d. magnitude of position vector

Coordinates of a point in the first octant are:
(Medium | NCERT)

a a. all negative b b. all positive c c. two positive d d. one positive

Reflection of $(2,-3,4)$ in the $xy$-plane is:
(Medium | NCERT)

a a. $(2,-3,-4)$ b b. $(-2,-3,4)$ c c. $(2,3,4)$ d d. $(-2,3,-4)$

Distance of $(3,4,12)$ from the origin is:
(Hard | NCERT)

a a. 13 b b. 12 c c. 5 d d. $\sqrt{169}$

Which point lies in the third octant?
(Hard | NCERT)

a a. $(1,2,3)$ b b. $(-1,-2,3)$ c c. $(-1,-2,-3)$ d d. $(1,-2,-3)$

Distance between $(1,2,3)$ and $(4,6,3)$ is:
(Hard | NCERT)

a a. 3 b b. 4 c c. 5 d d. 6

A point equidistant from all three axes satisfies:
(Hard | NCERT)

a a. $x=y=z$ b b. $x+y+z=0$ c c. $x^2=y^2=z^2$ d d. $x=y+z$

Distance of $(x,y,z)$ from the $y$-axis is:
(Hard | NCERT)

a a. $\sqrt{x^2+y^2}$ b b. $\sqrt{y^2+z^2}$ c c. $\sqrt{x^2+z^2}$ d d. $|y|$

A point in the $xy$-plane at distance 5 from the origin is:
(Hard | NCERT)

a a. $(3,4,0)$ b b. $(3,4,5)$ c c. $(0,5,5)$ d d. $(5,5,0)$

If $a=b=c$, the point $(a,b,c)$ lies on:
(Hard | NCERT)

a a. $x$-axis b b. space diagonal c c. $xy$-plane d d. $yz$-plane

Distance between $(2,-1,3)$ and $(2,-1,-3)$ is:
(Hard | NCERT)

a a. 6 b b. 3 c c. $\sqrt{36}$ d d. 0

Nearest point to the origin is:
(Hard | NCERT)

a a. $(2,2,2)$ b b. $(3,0,0)$ c c. $(1,1,1)$ d d. $(0,0,4)$

Distance from the origin remains unchanged under:
(Hard | NCERT)

a a. translation b b. reflection c c. rotation about the origin d d. scaling

Distance of $(a,b,c)$ from the $x$-axis is:
(Hard | NCERT)

a a. $\sqrt{a^2+b^2}$ b b. $\sqrt{b^2+c^2}$ c c. $\sqrt{a^2+c^2}$ d d. $|a|$

Point $(0,0,5)$ lies on:
(Easy | NCERT)

a a. $x$-axis b b. $y$-axis c c. $z$-axis d d. $xy$-plane

Distance of $(4,0,0)$ from the $yz$-plane is:
(Easy | NCERT)

a a. 0 b b. 4 c c. 16 d d. 2

A point with coordinates $(0,5,0)$ lies on:
(Easy | NCERT)

a a. $x$-axis b b. $y$-axis c c. $z$-axis d d. $yz$-plane

The octant containing $(-2,3,-4)$ is:
(Medium | NCERT)

a a. second b b. fourth c c. sixth d d. seventh

Distance between $(1,1,1)$ and $(-1,-1,-1)$ is:
(Medium | NCERT)

a a. 2 b b. $2\sqrt{3}$ c c. $\sqrt{6}$ d d. 3

A point lies on the $xy$-plane if:
(Easy | NCERT)

a a. $x=0$ b b. $y=0$ c c. $z=0$ d d. $x=y$

Distance of $(0,7,-24)$ from the $y$-axis is:
(Medium | NCERT)

a a. 7 b b. 24 c c. 25 d d. $\sqrt{49}$

A point equidistant from all three coordinate planes lies on:
(Medium | NCERT)

a a. axes b b. coordinate planes c c. space diagonal d d. origin only

Coordinates of a point on the $xz$-plane are:
(Easy | NCERT)

a a. $(x,y,0)$ b b. $(0,y,z)$ c c. $(x,0,z)$ d d. $(0,0,z)$

Distance between $(2,3,4)$ and $(2,3,4)$ is:
(Easy | NCERT)

a a. 1 b b. 0 c c. 4 d d. 9

A point at equal distance from the three axes satisfies:
(Hard | NCERT)

a a. $x=y=z$ b b. $x^2+y^2+z^2=0$ c c. $x^2=y^2=z^2$ d d. $x+y+z=0$

The distance of the origin from any coordinate plane is:
(Easy | NCERT)

a a. 1 b b. 0 c c. undefined d d. equal to axis length

A point $(a,0,0)$ is at distance $|a|$ from:
(Medium | NCERT)

a a. $yz$-plane b b. $xz$-plane c c. $xy$-plane d d. origin

Distance between $(0,3,4)$ and the origin is:
(Medium | NCERT)

a a. 3 b b. 4 c c. 5 d d. 7

Coordinates of a point common to both $xy$- and $yz$-planes are:
(Medium | NCERT)

a a. $(0,y,0)$ b b. $(x,0,0)$ c c. $(0,0,z)$ d d. $(0,0,0)$

Distance of $(5,-12,0)$ from the origin is:
(Medium | NCERT)

a a. 13 b b. 12 c c. 5 d d. $\sqrt{169}$

The plane $y=0$ represents:
(Easy | NCERT)

a a. $xy$-plane b b. $yz$-plane c c. $xz$-plane d d. $x$-axis

A point $(x,y,z)$ lies on the space diagonal if:
(Hard | NCERT)

a a. $x+y+z=0$ b b. $x=y=z$ c c. $x^2+y^2=z^2$ d d. $x=y$

The distance formula in three dimensions is based on:
(Hard | NCERT)

a a. similarity b b. congruence c c. Pythagoras theorem d d. coordinate transformation

📚

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

Sharing this chapter

Introduction To Three Dimensional Geometry | Maths Class 11

Introduction To Three Dimensional Geometry | Maths Class 11 — Complete Notes & Solutions · academia-aeternum.com

🎓 Class 11 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

Share on

X / Twitter

Facebook

Instagram

Threads

Quora

Discord

academia-aeternum.com/class-11/mathematics/introduction-to-three-dimensional-geometry/mcqs/ Copy link

💡

Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

Three Dimensional Geometry studies the position of points in space using three mutually perpendicular axes.

It involves three independent measurements represented by $x$, $y$, and $z$.

It is a reference framework consisting of three perpendicular axes intersecting at a common point.

The axes are the $x$-axis, $y$-axis, and $z$-axis.

The origin is the point where all three axes intersect and has coordinates $(0,0,0)$.

An ordered triplet $(x,y,z)$ represents the coordinates of a point in three dimensional space.

It represents the perpendicular distance of the point from the $yz$-plane.

It represents the perpendicular distance of the point from the $xz$-plane.

It represents the perpendicular distance of the point from the $xy$-plane.

The three coordinate planes are the $xy$-plane, $yz$-plane, and $zx$-plane.

The equation of the $xy$-plane is $z = 0$.

The equation of the $yz$-plane is $x = 0$.

The equation of the $zx$-plane is $y = 0$.

The distance is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$.

It is derived using the Pythagorean theorem extended to three dimensions.

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Practice Advance MCQs

Get in Touch

Let's Connect

Questions, feedback, or suggestions?
We'd love to hear from you.

Introduction to 3D Geometry

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Frequently Asked Questions

Q 01 What is Three Dimensional Geometry?

Q 02 Why is it called three dimensional?

Q 03 What is a coordinate system in 3D?

Q 04 What are the three coordinate axes?

Q 05 What is the origin in 3D geometry?

Q 06 What is an ordered triplet?

Q 07 What does the x-coordinate represent?

Q 08 What does the y-coordinate represent?

Q 09 What does the z-coordinate represent?

Q 10 What are coordinate planes in 3D geometry?

Q 11 What is the equation of the xy-plane?

Q 12 What is the equation of the yz-plane?

Q 13 What is the equation of the zx-plane?

Q 14 What is the distance formula between two points in 3D?

Q 15 How is distance formula derived?

Recent Posts