NEET Exam  >  NEET Notes  >  Physics Class 11  >  Vector & Scalar Quantities

Vector & Scalar Quantities | Physics Class 11 - NEET PDF Download

Mathematics and Science were invented by humans to understand and describe the world around us. A lot of mathematical quantities are used in Physics to explain the concepts clearly. A few examples of these include force, speed, velocity, and work. 

These quantities are often described as being a scalar or a vector quantity. 

  • Scalars and vectors are differentiated depending on their definition. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. 
  • On the other hand, a vector quantity is defined as the physical quantity that has both magnitudes as well as direction like force and weight. 
  • The other way of differentiating these two quantities is by using a notation. In this document, let us try to learn what is a vector and a scalar quantity.

What is a Scalar Quantity?

Scalar quantity is defined as the physical quantity with magnitude and no direction.

  • A scalar quantity only has a magnitude and a unit, it can be represented by a number only. A scalar does not have any direction.
    Example: Mass = 4 kg
  • The magnitude of mass = 4, Unit of mass = kg
  • Scalar quantities can be added, subtracted, and multiplied by simple laws of algebra.
  • Examples of Scalar Quantities: There are plenty of scalar quantity examples, some of the common examples are: Mass, Speed, Distance, Time, Area, Volume, Density & Temperature

Question for Vector & Scalar Quantities
Try yourself:Which of the following is a scalar quantity?
View Solution


What is a Vector

Quantity?

A vector quantity is defined as the physical quantity that has both direction as well as magnitude.

  • Vector is the physical quantities having magnitude as well as specified direction.Specified Direction
    Specified Direction
  • For example: Speed = 4 m/s (is a scalar), Velocity = 4 m/s toward north (is a vector).
  • If someone wants to reach some location, then it is not sufficient to provide information about the distance of that location it is also essential to tell him about the proper direction from the initial location to the destination.
  • The magnitude of a vector is the absolute value of a vector and is indicated by |A|.
  • Example of Vector quantity: Displacement, velocity, acceleration, force, etc.

Vector & Scalar Quantities | Physics Class 11 - NEET


Table: Difference between Vector and Scalar

Vector & Scalar Quantities | Physics Class 11 - NEET


General Points Regarding Vectors

1. Representation of Vector

  • Geometrically, the vector is represented by a line with an arrow indicating the direction of the vector as:

VectorVector

  • Mathematically, the vector is represented by Vector & Scalar Quantities | Physics Class 11 - NEET. Sometimes it is represented by the bold letter A.

Vector & Scalar Quantities | Physics Class 11 - NEET

  • Thus, the arrow in the above figure represents a vectorVector & Scalar Quantities | Physics Class 11 - NEET in XY-plane making an angle θ with the x-axis.
  • A representation of the vector will be complete if it gives us direction and magnitude.
  • Symbolic form: Vector & Scalar Quantities | Physics Class 11 - NEET used to separate a vector quantity from scalar quantities (u, i, m).
  • Graphical form: A vector is represented by a directed straight line, having the magnitude and direction of the quantity represented by it.
    Example: If we want to represent a force of 5 N acting 45° N of EVector & Scalar Quantities | Physics Class 11 - NEET(i) We choose direction coordinates.
    (ii) We choose a convenient scale like 1 cm = 1 N.
    (iii) We draw a line of length equal in magnitude and in the direction of vector to the chosen quantity.
    (iv) We put an arrow in the direction of the vector.

2. The Angle Between Two Vectors (θ)

The angle between two vectors means smaller of the two angles between the vectors when they are placed tail to tail by displacing either of the vectors parallel to itself.

Vector & Scalar Quantities | Physics Class 11 - NEET

3.  Negative of Vector

It implies vectors of the same magnitude but opposite in direction.

Negative vectorNegative vector

4. Equality of Vectors

Vectors having equal magnitude and same direction are called equal vectors.

Vector & Scalar Quantities | Physics Class 11 - NEET

Vector & Scalar Quantities | Physics Class 11 - NEET

5. Collinear Vectors

Any two vectors are collinear, then one can be expressed in terms of others. Vector & Scalar Quantities | Physics Class 11 - NEET = Vector & Scalar Quantities | Physics Class 11 - NEET (where λ is a constant)

Collinear vectorCollinear vector

Question for Vector & Scalar Quantities
Try yourself:What is the magnitude of a unit vector?
View Solution


6. Co-initial Vector

If two or more vectors start from the same point, then they called co-initial vectors.

Vector & Scalar Quantities | Physics Class 11 - NEET

Co-initial vector

Here A, B, C, D are co-initial vectors.


7. Coplanar Vectors


Three (or more) vectors are called coplanar vectors if they lie in the same plane or are parallel to the same plane. Two (free) vectors are always coplanar.

Coplanar VectorsCoplanar Vectors

Note:

If the frame of reference is translated or rotated the vector does not change (though its components may change).


8. Multiplication and Division of a Vector by a Scalar

  • Multiplying a vectorVector & Scalar Quantities | Physics Class 11 - NEET with a positive number λ gives a vectorVector & Scalar Quantities | Physics Class 11 - NEET whose magnitude becomes λ times, but the direction is the same as that ofVector & Scalar Quantities | Physics Class 11 - NEET.
    Multiplying a vectorVector & Scalar Quantities | Physics Class 11 - NEET by a negative number λ gives a vector Vector & Scalar Quantities | Physics Class 11 - NEET whose direction is opposite to the direction of  Vector & Scalar Quantities | Physics Class 11 - NEET and whose magnitude is λ times Vector & Scalar Quantities | Physics Class 11 - NEET.
  • The division of vector Vector & Scalar Quantities | Physics Class 11 - NEET by a non-zero scalar 'm' is defined as the multiplication of Vector & Scalar Quantities | Physics Class 11 - NEET by Vector & Scalar Quantities | Physics Class 11 - NEET
  • At here Vector & Scalar Quantities | Physics Class 11 - NEET and Vector & Scalar Quantities | Physics Class 11 - NEET are colinear vector.

9. Multiplication of a Vector

  • By a Real Number
    When a vector A is multiplied by a real number n, then its magnitude becomes n times but direction and unit remains unchanged.
  • By a Scalar
    When a vector A is multiplied by a scalar S, then its magnitude becomes S times, and unit is the product of units of A and S but direction remains same as that of vector A.

10. Scalar or Dot Product of Two Vectors

  • The scalar product of two vectors is equal to the product of their magnitudes and the cosine of the smaller angle between them. It is denoted by . (dot)
    A . B = AB cos θ
  • The scalar or dot product of two vectors is a scalar.

Properties of Scalar Product

  • Scalar product is commutative, i.e.,
    A . B= B . A
  • Scalar product is distributive, i.e.,
    A . (B + C) = A . B + A . C
  • Scalar product of two perpendicular vectors is zero.
    A . B = AB cos 90° = 0
  • Scalar product of two parallel vectors is equal to the product of their magnitudes, i.e., A . B = AB cos 0° = AB
  • Scalar product of a vector with itself is equal to the square of its magnitude, i.e.,
    A . A = AA cos 0° = A2
  • Scalar product of orthogonal unit vectors and Scalar product in cartesian coordinates
    = AxBx + AyBy + AzBz

Question for Vector & Scalar Quantities
Try yourself:Dot product of two mutual perpendicular vector is
View Solution


11. Vector or Cross Product of Two Vectors

  • The vector product of two vectors is equal to the product of their magnitudes and the sine of the smaller angle between them. It is denoted by X (cross).
    A X B = AB sin θ n
    Vector cross product
    Vector cross product
  • The direction of unit vector n can be obtained from right hand thumb rule.
  • If fingers of right hand are curled from A to B through smaller angle between them, then thumb will represent the direction of vector (A X B).
  • The vector or cross product of two vectors is also a vector.

Properties of Vector Product

  • Vector product is not commutative, i.e.,
    A X B ≠ B X A  [∴ (A X B) = - (B X A)]
  • Vector product is distributive, i.e.,
    A X (B + C) = A X B + A X C
  • Vector product of two parallel vectors is zero, i.e.,
    A X B = AB sin 0° = 0
  • Vector product of any vector with itself is zero.
    A X A = AA sin 0° = 0
  • Vector product of orthogonal unit vectors.
  • Vector product in cartesian coordinates.

Question for Vector & Scalar Quantities
Try yourself:The angle between the vectors (A x B) and (B x A) is:
View Solution


Direction of Vector Cross Product

  • When C = A X B, the direction of C is at right angles to the plane containing the vectors A and B. The direction is determined by the right hand screw rule and right hand thumb rule.
  • Right Hand Thumb Rule Curl the fingers of your right hand from A to B. Then, the direction of the erect thumb will point in the direction of A X B.
    Right Hand Thumb Rule
    Right Hand Thumb Rule
  • Right Hand Screw Rule Rotate a right handed screw from first vector (A) towards second vector (B). The direction in which the right handed screw moves gives the direction of vector (C).

The document Vector & Scalar Quantities | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
All you need of NEET at this link: NEET
118 videos|470 docs|189 tests

FAQs on Vector & Scalar Quantities - Physics Class 11 - NEET

1. What is a Scalar Quantity?
Ans. Scalar quantity refers to a physical quantity that is described as having only magnitude and no direction. Examples of scalar quantities are mass, temperature, energy, time, and volume.
2. What is a Vector Quantity?
Ans. A vector quantity refers to a physical quantity that has both magnitude and direction. Examples of vector quantities are displacement, velocity, acceleration, force, and momentum.
3. What are the general points regarding vectors?
Ans. Some general points regarding vectors are: - Vectors are represented by arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector. - Vectors can be added and subtracted using the parallelogram method, where the vectors are placed tail to tail and the diagonal of the parallelogram formed by the vectors represents the resultant vector. - The magnitude of a vector is always positive, but the direction can be positive, negative, or zero. - Vectors can be resolved into components along different axes, such as the x-axis and y-axis. - The dot product and cross product are two operations that can be performed on vectors.
4. What are some examples of scalar and vector quantities?
Ans. Some examples of scalar quantities are: - Mass - only has magnitude and no direction. - Temperature - only has magnitude and no direction. - Time - only has magnitude and no direction. - Energy - only has magnitude and no direction. - Volume - only has magnitude and no direction. Some examples of vector quantities are: - Displacement - has both magnitude and direction. - Velocity - has both magnitude and direction. - Acceleration - has both magnitude and direction. - Force - has both magnitude and direction. - Momentum - has both magnitude and direction.
5. What is the difference between scalar and vector quantities?
Ans. The main difference between scalar and vector quantities is that scalar quantities only have magnitude, while vector quantities have both magnitude and direction. Scalars can be added or subtracted by simple arithmetic, while vectors require vector addition using the parallelogram method. Scalars can be multiplied or divided by scalars or vectors, while vectors can only be multiplied or divided by scalars. Scalars are represented by numbers, while vectors are represented by arrows.
118 videos|470 docs|189 tests
Download as PDF
Explore Courses for NEET exam

How to Prepare for NEET

Read our guide to prepare for NEET which is created by Toppers & the best Teachers
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

Semester Notes

,

Vector & Scalar Quantities | Physics Class 11 - NEET

,

study material

,

Viva Questions

,

pdf

,

Previous Year Questions with Solutions

,

Important questions

,

Objective type Questions

,

video lectures

,

Free

,

MCQs

,

Vector & Scalar Quantities | Physics Class 11 - NEET

,

shortcuts and tricks

,

practice quizzes

,

Extra Questions

,

mock tests for examination

,

Exam

,

past year papers

,

Sample Paper

,

Vector & Scalar Quantities | Physics Class 11 - NEET

,

ppt

,

Summary

;