**12 class Maths Notes Chapter 10**

**Vector Algebra**

**free PDF| Quick revision**

**Vector Algebra**

**Notes class 12 maths**

**CBSE Revision Notes for CBSE Class 12 Mathematics Vector Algebra**Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

Class 12 Maths Chapter-10

**Vector Algebra**

**Quick Revision Notes Free Pdf**

**🔷 Chapter - 10 🔷**

**👉 Vector Algebra 👈**

**VECTORS**

**1. VECTORS & THEIR REPRESENTATION**

Vector quantities are specified by definite magnitude and definite directions. A vector is generally represented by a directed line segment, say AB. A is called the

**initial point**and B is called the

**terminal point**. The magnitude of vector AB is expressed by.

**1.1 Zero Vector**

A vector of zero magnitude is a zero vector i.e. which has the same initial & terminal point, is called a

**Zero Vector**. It is denoted by ö. The direction of zero vector is indeterminate.

**1.2 Unit Vector**

A vector of unit magnitude in direction of a vector a is called unit vector along a and is denoted by â symbolically â .

**1.3 Equal Vector**

Two vectors are said to be equal if they have the same magnitude, direction & represent the same physical quantity.

**1.4 Collinear Vector**

Two vectors are said to be collinear if their directed line segments are parallel disregards to their direction. Collinear vectors are also called

**Parallel Vectors**. If they have the same direction they are named as like vectors otherwise unlike vectors.

**1.5 Coplanar Vector**

A given number of vectors are called coplanar if their line segments are all parallel to the same plane. Note that

**"Two Vectors Are Always Coplanar".**

**1.6 Position Vector of A Point**

**2. ALGEBRA OF VECTORS**

**2.1 Addition of vectors**

**2.2 Multiplication of a Vector by a scalar**

**3. TEST OF COLLINEARITY**

**4. TEST OF COPLANARITY**

**5. PRODUCT OF VECTORS**

**5.1 Scalar product of two vectors**

**5.2 Vector product of two vectors**

**5.3 Scalar triple product**

**6. LINEAR COMBINATIONS**

**7. RECIPROCAL SYSTEM OF VECTORS**