Three Dimensional Geometry JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Three Dimensional Geometry are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

Three Dimensional Geometry is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
Three Dimensional Geometry in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Three Dimensional Geometry as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

Must Check News on JEE Main Maths:

Some of the most asked questions in the JEE Main exam for three-dimensional geometry include:

Distance between two points
Section formula
Direction ratios and direction cosines
Angle between two intersecting lines
Skew lines and shortest distance
Equations of a line and a plane
Intersection of a line and a plane
Coplanar lines

Three Dimensional GeometryJEE Mains Questions -

List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Question: Find the equation of a plane passing through the point (1, 2, 3) and parallel to the plane 2x + y - z = 5. This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) 2x + y - z = 0

· B) 2x + y - z = 1

· C) 2x + y - z = 10

· D) 2x + y - z = 15

Solution:

Since the required plane is parallel to the given plane, its normal will be the same. Using the point (1, 2, 3), the equation becomes 2x + y - z = 10. Correct answer is C.

Year: 2024

Question: What is the distance of the point (1, 2, 3) from the plane x + 2y + 2z = 9? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) 1

· B) 2

· C) 3

· D) 4

Solution:

The formula for distance from a point to a plane is |Ax₁ + By₁ + Cz₁ + D| / √(A² + B² + C²). Applying this formula, the distance is 3. Correct answer is C.

Year: 2022

Question:

The direction cosines of a line are l, m, n. Which of the following is always true? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) l² + m² = n²

· B) l² + m² + n² = 1

· C) l² - m² = n²

· D) l + m + n = 1

Solution:

For direction cosines, l² + m² + n² = 1 is always true. Correct answer is B.

Year: 2021

Question:

Find the equation of a line passing through (1, 2, 3) and parallel to the vector 2i + 3j + 4k. This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) (x - 1)/2 = (y - 2)/3 = (z - 3)/4

· B) (x + 1)/2 = (y + 2)/3 = (z + 3)/4

· C) (x - 1)/3 = (y - 2)/4 = (z - 3)/2

· D) None of these

Solution: Using the point and direction vector, the equation is (x - 1)/2 = (y - 2)/3 = (z - 3)/4. Correct answer is A.

Year: 2020

Question:

The angle between two lines with direction cosines l₁, m₁, n₁ and l₂, m₂, n₂ is given by? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) cosθ = l₁l₂ + m₁m₂ + n₁n₂

· B) cosθ = l₁ + m₁ + n₁

· C) cosθ = l₁ - l₂

· D) None of these

Solution: The angle between two lines is given by cosθ = l₁l₂ + m₁m₂ + n₁n₂. Correct answer is A.

Year: 2019

Question: What is the equation of the plane passing through the point (1, 0, 0) and perpendicular to the vector 3i - j + 2k? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) 3x - y + 2z = 3

· B) 3x - y + 2z = 0

· C) 3x + y - 2z = 1

· D) None of these

Solution

: The equation of the plane is given by 3(x - 1) - y + 2z = 0, which simplifies to 3x - y + 2z = 3. Correct answer is A.

Year: 2018

Question: The shortest distance between two skew lines is given by? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) |(a₁ - a₂) · (b₁ × b₂)| / |b₁ × b₂|

· B) |(a₁ + a₂) · (b₁ × b₂)| / |b₁ × b₂|

· C) (a₁ · a₂) / |b₁ × b₂|

· D) None of these

Solution:

The shortest distance between two skew lines is |(a₁ - a₂) · (b₁ × b₂)| / |b₁ × b₂|. Correct answer is A.

Year: 2017

Question:

The line x = y = z lies along which vector? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) i + j + k

· B) 2i + j + k

· C) i - j + k

· D) None of these

Solution: The direction ratios of the line x = y = z are 1:1:1, which corresponds to the vector i + j + k. Correct answer is A.

Year: 2016

Question:

Find the coordinates of the foot of the perpendicular from the point (1, 2, 3) to the plane x + y + z = 6. This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) (2, 2, 2)

· B) (1, 1, 1)

· C) (3, 2, 1)

· D) (1, 2, 3)

Solution: The coordinates of the foot of the perpendicular can be found using projection formula. Correct answer is B.

Year: 2015

Question: If a line has direction ratios proportional to 1, 2, 3, what are its direction cosines? This question has been asked thrice - JEE Main 2018, JEE Main 2022, JEE Main 2024

· A) 1/√14, 2/√14, 3/√14

· B) 1/√12, 2/√12, 3/√12

· C) 1, 2, 3

· D) None of these

Solution: The direction cosines are obtained by dividing the direction ratios by their magnitude, which is √14. Correct answer is A.

Year: 2014

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