OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22

OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-22(a), Exe-22(b), Exe-22(c),Self Revision and Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22

Class: 12th
Subject: Mathematics
Chapter  : Ch-22 Vectors 2 of Section -B
Board ISC
Writer  OP Malhotra, SK Gupta, Anubhuti Gangal
Publications S.Chand Publications 2020-21

-: Included Topics :-

Exe-22(a), 

Exe-22(b), 

Exe-22(c), 

Self Revision

Chapter Test


OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22

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

The various types of vectors included in vector algebra for class 12 concepts are

  • Zero Vector
  • Unit Vector
  • Position Vector
  • Co-initial Vectors
  • Collinear Vectors
  • Equal Vectors
  • Negative of a Vector

Zero Vector :- A zero vector is a vector when the magnitude of the vector is zero and the starting point of the vector coincides with the terminal point. In other words, for a vector A the co-ordinates of the point  are same as that of the point  then the vector is said to be a zero vector and is denoted by 0.

Unit Vector :-A vector which has a magnitude of unit length is called a unit vector. Suppose if x is a vector having a magnitude x then the unit vector is denoted by  in the direction of the vector  and has the magnitude equal to 1.

Position Vector :- If O is taken as reference origin and A is an arbitrary point in space then the vector  is called as the position vector of the point.

Position vector simply denotes the position or location of a point in the three-dimensional Cartesian system with respect to a reference origin.

Collinear Vectors :- Vectors which lie along the same line or parallel lines are known to be collinear vectors. They are also known as parallel vectors.

Equal Vectors :- Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

Negative of a Vector :- If two vectors are the same in magnitude but exactly opposite in direction then both the vectors are negative of each other. Assume there are two vectors a and b, such that these vectors are exactly the same in magnitude but opposite in direction then these vectors can be given by

= – b


Exe-22(a)

OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22


Exe-22(b)

Vectors 2 ISC Class-12 Maths Solutions Ch-22


Exe-22(c)

OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22


Self Revision

OP Malhotra Vectors 2 ISC Class-12 Maths Solutions Ch-22


Chapter Test

Vectors 2 ISC Class-12 Maths Solutions Ch-22


-: End of  Vectors 2 S. Chand ISC Class-12 Maths Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions


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