Three Dimensional Geometry for JEE

• l² + m² + n² = 1 for direction cosines
• Line: (x − x₁)/a = (y − y₁)/b = (z − z₁)/c
• Plane: ax + by + cz + d = 0 with normal (a, b, c)
• Skew lines are neither parallel nor intersecting

• Distance from point to plane: |ax₁ + by₁ + cz₁ + d|/√(a² + b² + c²)
• Shortest distance = |(b⃗ − a⃗)·(d₁ × d₂)| / |d₁ × d₂|
• Angle between planes: cosθ = |n₁·n₂|/(|n₁||n₂|)
• Foot of perpendicular via the parametric point

Printable Three Dimensional Geometry formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

• Using direction ratios as cosines
• Sign of d in plane distance
• Forgetting absolute value in angles

Appears in almost every JEE Main shift. With vectors, this is one of the most scoring Maths areas: 2–3 questions are common.

Prerequisites: Vector Algebra.

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Question. Two skew lines are given by L₁: (x−1)/2 = (y−2)/1 = (z−3)/3 and L₂: (x−4)/1 = (y−1)/2 = (z−2)/1. Find the equation of the plane containing L₁ and parallel to L₂. Also find the shortest distance between the two lines.

This example was solved twice independently and both solutions agree.

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

• THREE-DIMENSIONAL GEOMETRY in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:03:00
  Jump to a subtopic (26)

  • 00:00 Introduction
  • 04:46 Topics to be covered
  • 06:46 Coordinates for 3D Geometry
  • 08:36 Distance & Section Formula in 3D
  • 16:57 Angle bisector theorem
  • 43:30 Direction Ratios & Direction Cosines
  • 1:22:05 Equation of Lines in 3D
  • 1:45:52 Summary for equation of lines
  • 2:07:47 Image & Foot of Perpendicular on a line
  • 2:25:40 Shortest distance between skew lines
  • 2:48:52 Coplanar Lines
  • 3:04:15 Line of shortest distance
  • 3:22:40 Distance between parallel lines
  • 3:58:52 Various forms of planes
  • 4:35:57 Equation of Planes through 3 points
  • 4:42:27 Equation of Planes in 3D
  • 4:49:36 Another equation of plane
  • 4:54:22 Perpendicular distance between a point and plane
  • 5:04:43 Distance between parallel planes
  • 5:07:03 Image & Foot of Perpendicular in a Plane
  • 5:17:58 Angle between a line and plane
  • 5:25:05 Family of Planes
  • 5:36:20 Equation of line in asymmetrical form
  • 5:45:00 Equation of Spheres
  • 6:01:14 Homework
  • 6:01:48 Thankyou bachhon
• Vectors & 3D Geometry One Shot | JEE Main 2024 | RRR — JEE Nexus by Unacademy, 2:38:30
  Jump to a subtopic (10)

  • 0:00 Introduction
  • 3:15 Section formula
  • 33:08 Collinearity of vectors
  • 48:37 Dot product of vectors
  • 1:05:47 Rectangular Resolution of a vector
  • 1:08:50 Cross product of two vectors
  • 1:26:48 Triple product of vectors
  • 1:40:54 Concept of DC and DR
  • 1:45:57 Straight lines in 3D
  • 2:22:29 Distance of a point from a line and distance between two lines

• 17 JEE Main 2026 PYQs on Three Dimensional Geometry, with solutions.
• Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
• Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
• Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
• See it move: interactive simulation.