Mathematics · JEE

Important Questions: Three Dimensional Geometry for JEE

31+ syllabus-aligned questions available

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The most important Three Dimensional Geometry questions for JEE cover conceptual traps, standard results, and numerical patterns from 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. Goodmarks provides 31+ high-yield MCQs with full solutions.

Focus on what matters most. These important Three Dimensional Geometry questions cover high-weightage concepts from 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 — the topics JEE repeats every year.

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36+ important formulas for Three Dimensional Geometry

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Subtopics in Three Dimensional Geometry

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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 makes a Three Dimensional Geometry question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Three Dimensional Geometry are high-weightage?

Key areas include 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. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.