Mathematics · JEE

Three Dimensional Geometry Concepts for JEE

25+ syllabus-aligned questions available

Quick answer

Master Three Dimensional Geometry by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Three Dimensional Geometry before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Concept overview for Three Dimensional Geometry covering 3 JEE syllabus subtopics including Coordinates of a point in space, the distance between two points, section formula, Direction ratios and direction cosines and the angle between two intersecting lines, Equation of a line; Skew lines, the shortest distance between them and its equation.

Key points

Understand the definition and scope of Coordinates of a point in space, the distance between two points, section formula in the JEE syllabus
Memorise key formulas and standard results linked to Coordinates of a point in space, the distance between two points, section formula
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions
Understand the definition and scope of Direction ratios and direction cosines and the angle between two intersecting lines in the JEE syllabus
Memorise key formulas and standard results linked to Direction ratios and direction cosines and the angle between two intersecting lines
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Coordinates of a point in space, the distance between two points, section formula with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Coordinates of a point in space, the distance between two points, section formula and reattempt after 48 hours
Revise Direction ratios and direction cosines and the angle between two intersecting lines with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Direction ratios and direction cosines and the angle between two intersecting lines and reattempt after 48 hours

Common trap

Students often rush Coordinates of a point in space, the distance between two points, section formula questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

JEE Formula Sheet

36+ important formulas for Three Dimensional Geometry

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Subtopics in Three Dimensional Geometry

View Three Dimensional Geometry formula sheet — 36+ JEE formulas

Free sample questions

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Q1MathsUnit 11: Three Dimensional Geometry

The plane

\boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0}

and the line

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

are related as

Q2MathsUnit 11: Three Dimensional Geometry

Statement-1: The point

\boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6})

is the mirror image of the point

B(1,3,4)

in the plane

\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5}

Statement-2: The plane

\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5}

bisects the line segment joining

\boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6})

and

\boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4})

Q3MathsUnit 11: Three Dimensional Geometry

How many cubes each of surface area

24 c m^{2}

can be made out of a cube of edge measure

1 \mathrm{m} ?

Q4MathsUnit 11: Three Dimensional Geometry

In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are

Q5MathsUnit 11: Three Dimensional Geometry

The equation of the plane passing through the intersection of the planes

\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6}

and

\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}=

0,

and the point (1,1,1) is

Q6MathsUnit 11: Three Dimensional Geometry

Find the equation of the plane through the points

\boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2})

and

\boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6})

Q7MathsUnit 11: Three Dimensional Geometry

\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}=

\frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}}

are coplanar then

\mathbf{k}=?

Q8MathsUnit 11: Three Dimensional Geometry

The shortest distance between the lines

\frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}}

and

\frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}=

\frac{y-7}{-5}=\frac{z-5}{-5}

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Frequently asked questions

What concepts in Three Dimensional Geometry are essential for JEE?

Focus on core ideas across Coordinates of a point in space, the distance between two points, section formula, Direction ratios and direction cosines and the angle between two intersecting lines, Equation of a line; Skew lines, the shortest distance between them and its equation. JEE tests application, not just memorisation.