# Vectors ML Aggarwal ISC Class-12 Maths Solutions

Vectors ML Aggarwal ISC Class-12 Maths Solutions Chapter-1 Section-B. Step by step Solutions of ML Aggarwal ISC Class 12 Mathematics for Exercise Questions with Chapter Test. Visit official Website for detail information about ISC Board Class-12 Mathematics.

## Vectors ML Aggarwal ISC Class-12 Maths Solutions Chapter-1 Section-B

 Board ISC Class 12 Subject Mathematics Ch-1 Sec-B Vol-2 Vectors Session 2024-25 Topics Solutions of ML Aggarwal

### Vectors

Vector: Those quantities which have magnitude, as well as direction, are called vector quantities or vectors.  Those quantities which have only magnitude and no direction, are called scalar quantities.

Representation of Vector: A directed line segment has magnitude as well as direction, so it is called vector denoted as 𝐴𝐵⃗ or simply as 𝑎⃗ . Here, the point A from where the vector 𝐴𝐵⃗ starts is called its initial point and the point B where it ends is called its terminal point.

Magnitude of a Vector: The length of the vector 𝐴𝐵⃗ or 𝑎⃗  is called magnitude of 𝐴𝐵⃗ or 𝑎⃗  and it is represented by |𝐴𝐵⃗| or |𝑎⃗ | or a.
Note: Since, the length is never negative, so the notation |𝑎⃗ |< 0 has no meaning.

#### Types of Vectors

Null vector or zero vector: A vector, whose initial and terminal points coincide and magnitude is zero, is called a null vector and denoted as 0⃗ . Note: Zero vector cannot be assigned a definite direction or it may be regarded as having any direction. The vectors 𝐴𝐴⃗ , 𝐵𝐵 represent the zero vector.

Unit vector: A vector of unit length is called unit vector.

Collinear vectors: Two or more vectors are said to be collinear, if they are parallel to the same line, irrespective of their magnitudes and directions, e.g. 𝑎⃗  and 𝑏⃗  are collinear, when 𝑎⃗ =±𝜆𝑏⃗  or |𝑎|⃗=𝜆|𝑏|⃗

Coinitial vectors: Two or more vectors having the same initial point are called coinitial vectors.

Equal vectors: Two vectors are said to be equal, if they have equal magnitudes and same direction regardless of the position of their initial points. Note: If 𝑎⃗  = 𝑏⃗ , then |𝑎|⃗=|𝑏|⃗ but converse may not be true.

Negative vector: Vector having the same magnitude but opposite in direction of the given vector, is called the negative vector e.g. Vector 𝐵𝐴⃗ is negative of the vector 𝐴𝐵⃗ and written as 𝐵𝐴⃗ = – 𝐴𝐵⃗.
Note: The vectors defined above are such that any of them may be subject to its parallel displacement without changing its magnitude and direction. Such vectors are called ‘free vectors’.

#### Operations on Vectors

Vector Algebra includes addition, subtraction, and three types of multiplication between vectors. Below we will see how to perform addition on two vectors.

### Exercise – 1.1

Vectors ML Aggarwal ISC Class-12 Vol-2 Maths Solutions Chapter-1 Section-B

### Exercise – 1.2

Vectors ML Aggarwal ISC Class-12 Vol-2 Maths Solutions Chapter-1 Section-B

### Exercise – 1.3

Vectors ISC Class-12 Vol-2 Maths Solutions Chapter-1 Section-B

### Exercise – 1.4

Vectors ISC Class-12 Vol-2 Maths Solutions Chapter-1 Section-B

### Exercise – 1.5

Vectors Maths Solutions

### Chapter Test

Vectors ISC Class-12 Vol-2 Maths Solutions Chapter-1 Section-B

-: End of Vectors ML Aggarwal ISC Class-12 (Vol-II) Solutions  :-

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