Proven Strategies to Excel in JEE Main 2025-26 Three Dimensional Geometry Mock Tests
Three Dimensional Geometry is a pivotal chapter for JEE Maths, covering concepts such as equations of lines and planes, shortest distances, and direction ratios. Mastering this topic strengthens your spatial visualization and analytical skills essential for tackling advanced JEE questions. Attempt this focused mock test to reinforce your grasp and boost your confidence for the exam.
Mock Test Instructions for the Three Dimensional Geometry Mock Test 1-2:
- 20 questions from Three Dimensional Geometry Mock Test 1-2
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Strengthen Your Mastery of Three Dimensional Geometry?
- Bridge your conceptual gaps by practicing varied MCQs on lines, planes, and direction cosines.
- Identify recurring mistakes in applications of shortest distance and spatial vectors.
- Improve your speed through repeated, exam-like problems and timer-based practice.
- Track your progress with instant scoring and feedback for each 3D Geometry subtopic.
- Boost retention of formulas involving equations of planes, lines, and angle calculations in 3D space.
Sharpen Problem Solving in 3D Geometry with Vedantu’s JEE Chapterwise Mock Tests
- Master equations of planes and lines used in JEE Main questions.
- Apply the distance and angle formulae in real-exam simulated MCQs.
- Practice NTA pattern questions on spatial relationships for greater accuracy.
- Develop visualization skills necessary for advanced 3D geometry reasoning problems.
- Use result analysis for focused revision on weak 3D Geometry concepts.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
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| 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 the equation of a plane in three-dimensional geometry?
The general equation of a plane in three-dimensional geometry is Ax + By + Cz + D = 0, where A, B, and C are the direction ratios (coefficients) of the normal to the plane, and D is a constant.
2. How do you calculate the distance between a point and a plane?
The distance between a point (x1, y1, z1) and the plane Ax + By + Cz + D = 0 is given by:
Distance = |A x1 + B y1 + C z1 + D| / √(A2 + B2 + C2).
3. What are direction cosines and direction ratios?
The direction cosines (l, m, n) are the cosines of angles made by a line with the x, y, and z axes, respectively. The direction ratios are proportional values (a, b, c) that represent the direction of a line. They are related by the formula l = a/√(a2+b2+c2), and similarly for m and n.
4. How can you find the equation of a line passing through two points in 3D?
To find the equation of a line through P(x1, y1, z1) and Q(x2, y2, z2), use:
(x - x1)/(x2 - x1) = (y - y1)/(y2 - y1) = (z - z1)/(z2 - z1).
5. What is the vector form of the equation of a line in space?
The vector equation of a line passing through a point a and parallel to vector b is r = a + λb, where λ is a real parameter.
6. How do you determine if two lines in 3D are skew lines?
Two lines in 3D are called skew lines if they are not parallel and do not intersect at any point. Check:
- Direction ratios are not proportional (not parallel).
- Solving their equations yields no common solution (do not intersect).
7. What is the angle between two planes in three-dimensional geometry?
The angle (θ) between two planes is the angle between their normals. If the planes are A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0, then:
cosθ = (A1A2 + B1B2 + C1C2) / [√(A12 + B12 + C12) × √(A22 + B22 + C22)].
8. Can the distance between two skew lines be calculated?
Yes, the shortest distance (S) between two skew lines is given by:
S = |(a2 - a1) · (b1 × b2)| / |b1 × b2|, where a1 and a2 are position vectors, and b1, b2 are direction vectors of the two lines.
9. What is the condition for three points to be collinear in 3D?
Three points P, Q, and R in 3D are collinear if the vectors QR and PQ are proportional. This means their direction ratios are in the same ratio.
10. How do you find the equation of a plane passing through three non-collinear points?
To find the plane equation through points A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3):
- Form two vectors, say AB and AC.
- Find the cross product to get the normal vector.
- Use the point-normal plane equation.
11. What is the relationship between the direction cosines of a line?
For any line in three-dimensional geometry, the sum of the squares of its direction cosines is always 1: l2 + m2 + n2 = 1, where l, m, n are direction cosines.
12. How to check if a point lies on a given plane?
Substitute the coordinates of the point into the plane's equation. If the equation is satisfied (the result is 0), then the point lies on the plane.
