Proven Strategies to Excel in JEE Main Three Dimensional Geometry Mock Tests
Three Dimensional Geometry is a high-weightage chapter in JEE Maths, essential for acing questions on lines, planes, and spatial reasoning. This mock test covers direction cosines/ratios, equations of lines/planes, and shortest distance concepts, ensuring solid preparation for scoring maximum marks. Attempt the test now to reinforce your problem-solving skills and boost your confidence for the JEE Main exam!
Mock Test Instructions for the Three Dimensional Geometry Mock Test-3:
- 20 questions from Three Dimensional Geometry Mock Test-3
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Three Dimensional Geometry?
- Strengthen concepts of direction cosines, lines, and planes through real JEE-level mock questions.
- Identify weak spots in solving shortest distance and angle-based geometry problems.
- Improve visualization skills of 3D space by consistent chapter-wise practice.
- Develop the ability to solve typical examiner trick questions on coplanarity and perpendicularity.
- Boost time management skills by attempting MCQs in a fixed time frame for maximum accuracy.
Master Three Dimensional Geometry with Expert-Designed JEE Mock Tests
- Practice vector and Cartesian equations of lines and planes aligned with NTA JEE pattern.
- Refine calculation of direction ratios and projection formulas through targeted MCQs.
- Simulate actual exam conditions to reinforce problem-solving speed and confidence.
- Leverage instant feedback to focus revision on commonly missed concepts in 3D Geometry.
- Track improvement by retrying mock tests and analyzing trends in your performance analytics.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
|---|---|
| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
| 3 | Online FREE Mock Test for JEE Main Physics |
Important Study Materials Links for JEE Exams
FAQs on Three Dimensional Geometry Mock Test for JEE Main 2025-26 Preparation
1. What is a vector in three-dimensional geometry?
Vectors in three-dimensional geometry are quantities that have both magnitude and direction. They are typically represented as ordered triples (x, y, z) and can describe positions, displacements, or directions in 3D space.
2. How do you find the equation of a plane in 3D geometry?
The equation of a plane in three-dimensional geometry can be written as Ax + By + Cz + D = 0, where A, B, and C are the components of the normal vector to the plane, and D is a constant. Use the coordinates of a point on the plane and the normal vector to derive the specific equation for a given plane.
3. What is the distance formula between two points in space?
In 3D space, the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by:
Distance = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]. This formula extends the Pythagorean Theorem to three dimensions.
4. What is the direction cosine in three-dimensional geometry?
The direction cosines are the cosines of the angles that a vector makes with the positive x, y, and z axes. If l, m, and n are the direction cosines of a vector, then l² + m² + n² = 1.
5. How do you determine if two lines in space are parallel, perpendicular, or skew?
Two lines in 3D space are:
- Parallel if their direction ratios are proportional.
- Perpendicular if the sum of the products of their corresponding direction ratios is zero.
- Skew if they are neither parallel nor intersecting.
6. What is the scalar (dot) product of two vectors in 3D?
The scalar product or dot product of two vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃) is given by a · b = a₁b₁ + a₂b₂ + a₃b₃. It measures the extent to which two vectors point in the same direction.
7. How do you calculate the shortest distance between two skew lines in 3D?
The shortest distance between two skew lines is given by:
Distance = |(a₂ - a₁) · (d₁ × d₂)| / |d₁ × d₂|,
where a₁ and a₂ are position vectors on each line and d₁, d₂ are their direction vectors. Use the cross product to find the vector perpendicular to both lines, then project the difference vector onto it.
8. What are the conditions for coplanarity of points in three dimensions?
Four points A, B, C, and D in 3D space are coplanar if the scalar triple product of the vectors AB, AC, and AD is zero. In symbols, [AB, AC, AD] = 0 indicates coplanarity.
9. How can you determine the equation of a line passing through two points in space?
The equation of a line passing through two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is:
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁) = (z - z₁)/(z₂ - z₁). This is known as the symmetrical form of a line equation in three-dimensional geometry.
10. What is the vector product (cross product) of two vectors?
The vector product or cross product of vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃) is a vector given by:
a × b = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁). It is perpendicular to both a and b and its magnitude equals the area of the parallelogram formed by a and b.
11. What is the angle between two planes in three-dimensional geometry?
The angle between two planes is given by the angle between their normal vectors. If n₁ and n₂ are normal vectors, then:
cos θ = |(n₁ · n₂)| / (|n₁||n₂|),
where θ is the angle between the planes.
12. How do you find the foot of the perpendicular from a point to a given plane?
To find the foot of the perpendicular from point P(x₁, y₁, z₁) to plane Ax + By + Cz + D = 0:
- Let the foot be Q(x, y, z).
- Parametrically express Q along the normal: (x, y, z) = (x₁, y₁, z₁) + λ(A, B, C).
- Substitute Q into the plane equation and solve for λ.
- Find actual coordinates using the value of λ.
