Goodmarks

Mathematics · JEE

Important Questions: Three Dimensional Geometry for JEE

16+ syllabus-aligned questions available

Quick answer

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 16+ 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.

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

Attempt 8 free MCQs for Three Dimensional Geometry. Unlock 8+ more with Pro.

Unlock full bank
Q1MathsUnit 11: Three Dimensional Geometry
The plane x−2y+z−6=0\boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0} and the line x1=y2=z3\frac{x}{1}=\frac{y}{2}=\frac{z}{3} are related as
Q2MathsUnit 11: Three Dimensional Geometry
Statement-1: The point A(3,1,6)\boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) is the mirror image of the point B(1,3,4)B(1,3,4) in the plane x−y+z=5\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} Statement-2: The plane x−y+z=5\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} bisects the line segment joining A(3,1,6)\boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) and B(1,3,4)\boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4})
Q3MathsUnit 11: Three Dimensional Geometry
How many cubes each of surface area 24cm224 c m^{2} can be made out of a cube of edge measure 1m?1 \mathrm{m} ?
Q4MathsUnit 11: Three Dimensional Geometry
Find the equation of the plane through the points A(2,2−1),B(3,4,2)\boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2}) and C(7,0,6)\boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6})
Q5MathsUnit 11: Three Dimensional Geometry
The shortest distance between the lines x−54=y−7−5=z+3−5\frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}} and x−84=\frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}= y−7−5=z−5−5\frac{y-7}{-5}=\frac{z-5}{-5} is
Q6MathsUnit 11: Three Dimensional Geometry
Let⁡A(2i^+3j^+5k^)B(−i^+3j^+2k^)\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(λi^+5j^+μk^)C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k}) are vertices of aa triangle and its median through AA is equally inclined to the positive directions of the axes. The value of λ+\lambda+ μ\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

Want unlimited Three Dimensional Geometry practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started freeView Pro plans

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.

Related topics