jee_main_2024_30_january_evening - Three Dimensional Geometry Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

QUESTION #13 Lines in Space
Let L₁: r = ( i - j +2 k) + λ ( i - j +2 k),λ in R L₂: r = ( j - k) + μ (3 i + j +p k),μ in R and L₃: r = δ ( i + m j + n k) δ in R Be three lines such that L₁ is perpendicular to L₂ and L₃ is perpendicular to both L₁ and L₂ . Then the point which lies on L₃ is
Start Practice →
QUESTION #22 Lines in Space
Let a line passing through the point (-1, 2, 3) intersect the lines L₁: (x - 1)/(3) = (y - 2)/(2) = (z + 1)/(-2) at M(α, β, γ) and L₂: (x + 2)/(-3) = (y - 2)/(-2) = (z - 1)/(4) at N(a, b, c). Then the value of ((α + β + γ)²)/((a + b + c)²) equals
Start Practice →
Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

Select Your Target Exam

Choose an exam track below to find formulas per chapter and patterns.

Syncing Exam Intelligence

Mapping formulas and patterns across all tracks…

PATH A — FULL LENGTH PRACTICE

Full Mock Test Hub

Simulate real NTA exam conditions with fully tracked mocks. Time yourself against past papers.

Now Live Open
PATH B — TARGETED PRACTICE

Topic-wise Practice Hub

Practice past-year questions one chapter at a time. Pick an exam → subject → chapter and get every PYQ for that topic — pulled together from all past papers — with the chapter's key formulas alongside.

Loading Questions... Browse Topics

Exam Analysis Tools

Chapter weightage trends and topic-wise practice — all mapped from past shift papers.

Year-wise PYQ

Chapter Weightage & Trends

See high-yield chapters, year-wise counts and the frequency-based chance each topic repeats next exam.

Weightage Board Open
Targeted PYQs

Topic-wise Practice Hub

Every past-year question for a chapter pulled from all papers, with its key formulas alongside.

One chapter at a time Open
Latest from the Blog
View all →

Loading articles...