Important Formulas and Solved Examples for 3D Geometry Mock Test
Three Dimensional Geometry is pivotal in JEE Main Maths, testing your grasp of lines, planes, and their intersections in space. Mastering this chapter boosts your spatial reasoning and strengthens problem-solving for key concepts like direction cosines, shortest distances, and equation of lines and planes. Attempt this focused mock test now to reinforce your 3D Geometry fundamentals and power up your JEE 2025 score!
Mock Test Instructions for the Three Dimensional Geometry Mock Test 1:
- 20 questions from Three Dimensional Geometry
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How JEE Mock Tests Help You Master Three Dimensional Geometry
- Identify your weak areas in lines, planes, and shortest distance with targeted 3D Geometry MCQs.
- Practise previous year PYQ-style problems to build real-exam readiness.
- Time-bound mock tests improve accuracy, speed, and conceptual clarity.
- Analyze instant feedback to resolve misconceptions on direction cosines and planes.
- Mock tests ensure complete coverage of all 3D Geometry concepts vital for JEE Main 2025.
Excel in JEE 2025 Three Dimensional Geometry With Practice Designed by Experts
- Work through exam-level questions on intersection of planes and 3D vectors.
- Strengthen spatial visualization and understand equations of lines in space via expert-created quizzes.
- Track your progress to focus revision on direction ratios and distances between skew lines.
- Build confidence with instant scoring and correction after each attempt.
- Bridge your learning gaps with focused practice on common errors in 3D Geometry questions.
Subject-Wise Excellence: JEE Main Mock Test Links
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| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
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Important Study Materials Links for JEE Exams
FAQs on Three Dimensional Geometry Mock Test 2025-26: Practice Questions & Solutions
1. What is a vector in three-dimensional geometry?
A vector in three-dimensional geometry is a quantity that has both magnitude and direction. It is usually represented as an ordered triplet (x, y, z) and illustrated by an arrow pointing from one point to another in space.
2. How do you find the distance between two points in 3D space?
To find the distance between two points, use the formula: Distance = √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²], where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points in three-dimensional space.
3. What is the equation of a plane in three dimensions?
The general form of the equation of a plane in three dimensions is: Ax + By + Cz + D = 0, where A, B, and C are the direction ratios of the normal to the plane, and D is a constant.
4. How do you determine if three points are collinear in 3D?
To check collinearity of three points in 3D geometry, calculate the vectors between each pair and verify if one vector is a scalar multiple of the other. If so, the points are collinear.
5. What is the formula for the direction cosines of a line?
The direction cosines of a line are the cosines of the angles the line makes with the x, y, and z axes, denoted as l, m, n. They satisfy the relation: l² + m² + n² = 1.
6. How do you find the angle between two lines in three-dimension?
The angle θ between two lines whose direction ratios are (a₁, b₁, c₁) and (a₂, b₂, c₂) is calculated by: cosθ = (a₁a₂ + b₁b₂ + c₁c₂) / [√(a₁² + b₁² + c₁²) × √(a₂² + b₂² + c₂²)].
7. What is the shortest distance between two skew lines?
The shortest distance between two skew lines is given by the formula: |(a2 - a1) • (d1 × d2)| / |d1 × d2|, where a1 and a2 are position vectors of points on each line, and d1, d2 are their direction vectors.
8. How is the equation of a line in 3D written in vector form?
The vector equation of a line that passes through point A (position vector a) and is parallel to vector b is: r = a + λb, where λ is a real parameter.
9. What does the scalar triple product of vectors represent?
The scalar triple product of vectors a, b, and c is a • (b × c). It gives the volume of the parallelepiped formed by the three vectors. If the result is zero, the vectors are coplanar.
10. How do you check if a point lies in a given plane?
To check if a point (x, y, z) lies in the plane Ax + By + Cz + D = 0, substitute the point's coordinates into the equation. If the equality holds true, the point lies on the plane.
11. What are direction ratios and how are they different from direction cosines?
Direction ratios of a line are any set of three numbers proportional to its direction cosines. Direction ratios help describe the orientation of a line but are not necessarily unit vectors, while direction cosines always are.
12. Explain the concept of coplanarity of vectors in 3D geometry.
Vectors are said to be coplanar if they lie in the same plane. This happens when their scalar triple product (a • (b × c)) is zero, indicating that the vectors are linearly dependent.
