Mathematics · JEE

Online Practice: Three Dimensional Geometry for JEE

16+ syllabus-aligned questions available

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Goodmarks provides free online JEE practice for Three Dimensional Geometry with 16+ 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 16+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

Subtopics in Three Dimensional Geometry

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

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

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})

Q5MathsUnit 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}

Q6MathsUnit 11: Three Dimensional Geometry

\operatorname{Let} \boldsymbol{A}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}) \boldsymbol{B}(-\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}})

and

C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k})

are vertices of

a

triangle and its median through

A

is equally inclined to the positive directions of the axes. The value of

\lambda+

\mu

is equal to

Q7MathsUnit 11: Three Dimensional Geometry

The ratio of the volume and surface area of a sphere of unit radius:

Q8MathsUnit 11: Three Dimensional Geometry

The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose direction ratios are 2,-3,6 is

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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 16+ 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.