Vector Algebra for JEE

• Dot product measures projection; zero for perpendicular vectors
• Cross product is perpendicular to both; magnitude = area of parallelogram
• Scalar triple product = volume of parallelepiped
• Coplanar vectors: [a b c] = 0

• a·b = |a||b| cosθ
• |a × b| = |a||b| sinθ
• Projection of a on b = a·b/|b|
• a × (b × c) = (a·c)b − (a·b)c

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

• Cross product order (a × b = −b × a)
• Using dot product for area
• Wrong expansion of vector triple product

Appears in almost every JEE Main shift. Quick, formula-driven questions. Combine with 3D geometry.

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

Question. Let a = 2i + j - k and b = i - 2j + 2k. If c is a vector such that a · c = |c|, |c - a| = 2√2, and the angle between (a × b) and c is 30°, find |c|.

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.

• VECTORS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:46:33
  Jump to a subtopic (24)

  • 00:00 Introduction
  • 06:35 Topics to be covered
  • 07:46 Null, Equal and Unit vector
  • 21:50 Position vectors
  • 33:13 Collinear vectors
  • 48:56 Vector law of Addition
  • 1:09:08 Parallelogram law
  • 1:10:32 Vector along angle bisector
  • 1:25:20 Dot Product
  • 2:22:19 Component of a vector along other vector
  • 2:43:53 Cross Product
  • 3:05:40 Area of a Parallelogram
  • 3:20:55 Area of a Quadrilateral
  • 3:28:10 Trick for Cross Product
  • 4:09:45 Linear Combination in a Plane
  • 4:30:17 Linear Combination in space
  • 4:31:56 Scalar Triple Product (STP)
  • 4:35:52 Properties of STP
  • 5:44:16 Vector Triple Product (VTP)
  • 5:58:47 Vector Product of 4 Vectors
  • 6:06:39 Scalar Product of 4 Vectors
  • 6:12:21 Solving Vector Equations
  • 6:43:35 Homework
  • 6:45:59 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

• 10 JEE Main 2026 PYQs on Vector Algebra, 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.