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3d Geometry Questions

Practice 76 3d Geometry questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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76
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0
Easy
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69
Medium
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7
Hard
Practice by Exam:Mathematics(68)Quantitative Aptitude(3)Reasoning(2)Logical Reasoning(1)Quantitative Aptitude@NUM: 54(1)Quantitative Aptitude@NUM: 52(1)

About 3D Geometry — practice questions, PYQs & concepts

3D Geometry is a frequently-tested topic on Mathematics, Quantitative Aptitude, Reasoning. ExamTest.live currently lists 76 3D Geometry questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

3D Geometry weight in competitive exams

Across our 3D Geometry question bank, the largest sources are Mathematics (68), Quantitative Aptitude (3), Reasoning (2), Logical Reasoning (1) and Quantitative Aptitude@NUM: 54 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 easy 3D Geometry questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
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All 3d Geometry Questions(1–76 of 76)

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Q1mediummcqMathematicsMathematics Mock Test - 52026
15% accuracy
What is the perpendicular distance from the point to the line ?
Q2mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The triangle formed by the points and is:
Q3mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
Let the line lie in the plane . The value of is:
Q4hardmcqMathematicsMathematics Mock Test - 102026
0% accuracy
The equation of a plane passing through the line of intersection of the planes and and at a distance from the point is . The value of is:
Q5mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
The lines and are perpendicular to each other, if:
Q6mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
The ratio in which the line segment joining the points and is divided by the -plane is:
Q7mediummcqLogical ReasoningCompetitive Exam2026
0% accuracy
If you have a regular dodecahedron and you slice it in half along a plane that passes through the centres of opposite faces, what is the shape of the cross-section?
Q8mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Find the shortest distance between the lines and .
Q9mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Find the image of the point in the plane .
Q10mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
A straight line with direction cosines is:
Q11mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
The plane makes an angle with the X-axis. The value of is equal to:
Q12mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Which of the following is NOT a known factor to uniquely determine a plane?
Q13mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Determine the coordinates of the point where the line through the points and crosses the -plane.
Q14mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If is the acute angle between the diagonals of a cube, then which one of the following is correct?
Q15mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
The length of the perpendicular drawn from the origin to the plane is:
Q16mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If a line has direction ratios , then what is the sum of the squares of its direction cosines?
Q17mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Find the angle between the pair of lines and .
Q18mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Determine the coordinates of the foot of the perpendicular drawn from the origin to the plane .
Q19mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If is the equation of the line passing through and , then is:
Q20mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
If the lines and lie on the same plane, then:
Q21mediummcqMathematicsAIEEE 20062026
0% accuracy
The image of the point in the plane is:
Q22mediummcqMathematicsAIEEE 20062026
0% accuracy
The two lines ; and are perpendicular to each other if:
Q23hardmcqMathematicsAIEEE 20042026
0% accuracy
If the straight lines and with parameters and respectively, are co-planar then equals
Q24hardmcqMathematicsAIEEE 20042026
0% accuracy
A line makes the same angle with each of the and axes. If the angle which it makes with -axis, is such that then equals
Q25hardmcqMathematicsAIEEE 20042026
0% accuracy
A line with direction cosines proportional to meets each of the lines and The co-ordinates of each of the point of intersection are given by
Q26hardmcqMathematicsAIEEE 20042026
0% accuracy
Distance between two parallel planes and is
Q27hardmcqMathematicsAIEEE 20042026
0% accuracy
The intersection of the spheres and is the same as the intersection of one of the sphere and the plane
Q28mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
Find the distance between the straight line and the plane .
Q29mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Find the Cartesian equation of the plane which passes through the point and is perpendicular to the line with direction ratios ?
Q30mediummcqMathematicsMathematics Mock Test - 112026
Let be a line that is perpendicular to the plane and passes through the point . The point on the line that is nearest to the -axis is:
Q31mediummcqMathematicsMathematics Mock Test - 112026
Three vertices of a parallelogram are , and . The coordinates of the fourth vertex are:
Q32mediummcqQuantitative Aptitude@NUM: 52SSC CGL2026
How many spherical balls each of radius can be made out of a solid metallic cube of edge ? (Take )
Q33mediummcqMathematicsMathematics Mock Test - 112026
Consider a plane passing through the points , and . Which one of the following points lies on this plane?
Q34mediummcqMathematicsMathematics Mock Test - 112026
Consider the plane passing through the points , and . What are the direction ratios of the normal to the plane?
Q35mediummcqMathematicsMathematics Mock Test - 112026
A line joining the points and is perpendicular to a plane. Then the coefficients of and in the equation of the plane are respectively:
Q36mediummcqMathematicsMathematics Mock Test - 112026
If the coordinates of and are and , then the projections of the line segment on the coordinate axes are:
Q37mediummcqMathematicsMathematics Mock Test - 112026
The number of straight lines that are equally inclined to the three-dimensional coordinate axes is:
Q38mediummcqMathematicsMathematics Mock Test - 112026
Let be the plane passing through the intersection of planes and . If the plane contains the origin, then the equation of the plane is:
Q39mediummcqMathematicsMathematics Mock Test - 112026
The reflection of the origin in the plane is:
Q40mediummcqReasoningCompetitive Exam2026
When a cylinder is sliced by a plane parallel to its height and passing through the center, what is the shape of the cross-section?
Q41mediummcqReasoningCompetitive Exam2026
A regular dodecahedron is sliced by a plane passing through two opposite edges and not through any vertices. What is the shape of the cross-section?
Q42mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Six solid cubes, each of side , are melted to form a rectangular solid of base area . The lateral surface area (in ) of the resulting solid is:
Q43mediummcqQuantitative Aptitude@NUM: 54Competitive Exam2026
A rectangle of length and breadth is rotated about its shorter side to form a cylinder. What is the volume (in ) of the cylinder so generated? (Take )
Q44mediummcqQuantitative AptitudeCompetitive Exam2026
How many cubes of length 50 cm can be accommodated in a container of 5 m in length, 2 m in width and 5 m in height?
Q45mediummcqQuantitative AptitudeCompetitive Exam2026
Find the maximum length of a rod, that can be placed in a room of dimension 12m×12m×14m.
Q46mediummcqMathematicsAIEEE2026
If the angle between the line and the plane is such that , then the value of is:
Q47mediummcqMathematicsAIEEE2026
A line in three-dimensional space makes angles and with the positive -axis and the positive -axis respectively. If makes an acute angle with the positive -axis, then equals:
Q48mediummcqMathematicsAIEEE2026
The angle between the lines and is:
Q49mediummcqMathematicsAIEEE2026
If the plane passes through the midpoint of the line joining the centres of the spheres and , then equals:
Q50mediummcqMathematicsAIEEE2026
The distance between the line and the plane is:
Q51mediummcqMathematicsAIEEE2026
The plane cuts the sphere in a circle of radius:
Q52mediummcqMathematicsAIEEE-CBSE-ENG-032026
A tetrahedron has vertices at , , and . Then the angle between the faces and will be:
Q53mediummcqMathematicsAIEEE-CBSE-ENG-032026
The radius of the circle in which the sphere is cut by the plane is:
Q54mediummcqMathematicsAIEEE-CBSE-ENG-032026
The lines and are coplanar if:
Q55mediummcqMathematicsAIEEE-CBSE-ENG-032026
The two lines , and , will be perpendicular, if and only if:
Q56mediummcqMathematicsAIEEE-CBSE-ENG-032026
The shortest distance from the plane to the sphere is:
Q57mediummcqMathematicsAIEEE-CBSE-ENG-032026
Two systems of rectangular axes have the same origin. If a plane cuts them at distances and from the origin, then:
Q58mediummcqMathematicsAIEEE2026
The line passing through the points and crosses the -plane at the point . Then:
Q59mediummcqMathematicsAIEEE2026
If the straight lines and intersect at a point, then the integer is equal to:
Q60mediummcqMathematicsAIEEE 20092026
Let the line lies in the plane . Then equals:
Q61mediummcqMathematicsAIEEE2026
Statement-1: The point is the mirror image of the point in the plane .Statement-2: The plane bisects the line segment joining and .
Q62mediummcqMathematicsMathematics Mock Test - 82026
If the plane is parallel to the line , then the value of is:
Q63hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If the angle between the line and the plane is , then equals:
Q64mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Statement-1 : The point is the mirror image of the point in the line .Statement-2 : The line bisects the line segment joining and .
Q65mediummcqMathematicsAIEEE 20122026
An equation of a plane parallel to the plane and at a unit distance from the origin is:
Q66mediummcqMathematicsAIEEE 20122026
If the lines and intersect, then is equal to:
Q67mediummcqMathematicsJEE Main2026
If the lines and are coplanar, then can have:
Q68mediummcqMathematicsJEE Main2026
Distance between two parallel planes and is:
Q69mediummcqMathematicsMathematics Mock Test - 32026
What is the cosine of the angle between the planes and ?
Q70mediummcqMathematicsMathematics Mock Test - 32026
The lines and are:
Q71mediummcqMathematicsMathematics Mock Test - 32026
The line with direction ratios is inclined with the -axis at an angle of:
Q72mediummcqMathematicsMathematics Mock Test - 82026
Determine the direction cosines of the unit vector perpendicular to the plane passing through the origin?
Q73mediummcqMathematicsMathematics Mock Test - 82026
Determine the vector equation for the line, given the Cartesian equation is ?
Q74mediummcqMathematicsMathematics Mock Test - 82026
Determine the vector equation of the plane passing through the intersection of the planes and , and through the point ?
Q75mediummcqMathematicsMathematics Mock Test - 82026
If from a point , perpendiculars and are drawn to the and planes respectively, then the equation of the plane (where is the origin) is:
Q76mediummcqMathematicsMathematics Mock Test - 82026
The ratio in which the plane divides the line joining the points and is:

Frequently Asked Questions

How many 3d Geometry questions are on ExamTest.live?▼
We have 76 3d Geometry questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are 3d Geometry MCQs free?▼
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Which exams include 3d Geometry questions?▼
3d Geometry questions are commonly asked in Mathematics, Quantitative Aptitude, Reasoning, Logical Reasoning, Quantitative Aptitude@NUM: 54. You can filter by exam using the links above.
How do I practice 3d Geometry questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.