Mathematics · JEE

Online Practice: Three Dimensional Geometry for JEE

31+ syllabus-aligned questions available

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Goodmarks provides free online JEE practice for Three Dimensional Geometry with 31+ MCQs, instant answer checking, and full solutions. Sign up to unlock the complete question bank and topic-wise filters.

Sharpen your mathematics preparation with interactive online practice for Three Dimensional Geometry. Goodmarks offers 31+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

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

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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

How do I practice Three Dimensional Geometry online for JEE?

Open this page, attempt the free sample MCQs, then sign up on Goodmarks to access the full Three Dimensional Geometry question bank with topic filters and detailed explanations.

How many Three Dimensional Geometry questions are available?

Goodmarks currently has 31+ JEE-aligned MCQs for Three Dimensional Geometry, with more added regularly.

Is this aligned with the JEE Main syllabus?

Yes. All Mathematics questions on Goodmarks are organised by official JEE Main units and 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.

Do I get solutions after each question?

Every question includes the correct answer and a step-by-step explanation. Free users can practise a random mix; Pro unlocks full subject and topic filters.