**1. Understand the Syllabus and Weightage**

**Key Topics to Cover:**- Basics of Vectors: Magnitude and direction
- Types of Vectors: Unit vector, Zero vector, Position vector
- Addition and Subtraction of Vectors
- Scalar (Dot) Product and its properties
- Vector (Cross) Product and its properties
- Applications: Angle between two vectors, Projection of a vector
- Scalar Triple Product (STP)

**Weightage in JEE Mains**:- Vector Algebra carries
**2-3 questions**, equivalent to**8-12 marks**.

- Vector Algebra carries

**2. Step-by-Step Study Plan**

**Step 1: Learn the Basics (Day 1-3)**

**Concepts to Master:**- Magnitude, Unit vectors, Position vectors
- Types of vectors (Collinear, Coplanar, etc.)
- Vector addition and subtraction

**Practice:**- Solve basic problems from
**NCERT and RD Sharma**to build a foundation. - Understand
**graphical representation**of vector addition and parallelogram law.

- Solve basic problems from

**Step 2: Master Dot Product (Day 4-6)**

**Concepts:**- Formula: $a⋅b=∣a∣∣b∣cosθ$
- Angle between two vectors
- Properties: Commutative, Distributive
- Applications: Work done by force (in physics)

**Practice:**- Solve conceptual questions on
**angles**and**orthogonal vectors**. - Use
**NCERT Exemplar**or**HC Verma (Physics)**for application-based problems.

- Solve conceptual questions on

**Step 3: Master Cross Product (Day 7-9)**

**Concepts:**- Formula: $a×b=∣a∣∣b∣sinθn^$
- Right-hand rule for direction of cross product
- Properties: Anti-commutative, Distributive
- Applications: Area of parallelogram and triangle

**Practice:**- Solve numerical problems on
**vector products**from**Arihant or Cengage**. - Try problems where
**unit vector components**are used.

- Solve numerical problems on

**Step 4: Learn Scalar Triple Product (STP) (Day 10-12)**

**Concepts:**- Formula: $a⋅(b×c)$
- Applications: Volume of parallelepiped, coplanarity condition.
- STP is
**zero**if vectors are coplanar.

**Practice:**- Solve problems involving
**volume and coplanarity**conditions. - Use
**JEE Advanced Previous Papers**for STP-related questions.

- Solve problems involving

**Step 5: Solve Previous Year Questions (Day 13-15)**

**Importance:**- This will give you a clear idea of
**the pattern of questions**asked in JEE Mains.

- This will give you a clear idea of
**Sources:**- Use
**Arihant’s 40 Years JEE Mains & Advanced**book or**Embibe**for topic-wise PYQs.

- Use

**Step 6: Take Mock Tests & Sectional Tests (Weekly)**

- Take
**sectional tests**to get accustomed to**time management**. - Analyze your mistakes and note down
**tricky formulas or concepts**. - Use
**NTA Abhyas App**or**Allen mock tests**to simulate real-exam scenarios.

**3. Study Materials and Books**

**NCERT Mathematics (Class 11 and 12)**– For conceptual clarity**Arihant Skills in Mathematics – Vectors & 3D Geometry****Cengage Mathematics**– For practice and advanced questions**Previous Year JEE Papers**– Practice regularly to build confidence

**4. Revision and Formula Sheet**

- Prepare a
**formula sheet**with all important properties:**Dot Product**: $a⋅b=∣a∣∣b∣cosθ$**Cross Product**: $a×b=∣a∣∣b∣sinθn^$**STP**: $a⋅(b×c)$ = Volume of parallelepiped.

**Quick Tip**: Revise this formula sheet regularly, especially in the last month before the exam.

**5. Key Tips for Success**

**Visualize concepts**: Graphically understand vector operations like addition, cross product, etc.**Practice consistently**: Don’t skip daily practice—15-20 vector problems per day will suffice.**Use error logs**: Keep track of mistakes made during tests and correct them.**Focus on conceptual clarity**: Avoid rote learning; understand the why behind formulas.**Stay motivated and consistent**: Set small goals and track progress weekly.

By following this plan and practicing regularly, you can easily master **Vector Algebra** and secure marks in IIT JEE Mains 2025. Let me know if you need any further help!