In this post we discussed about What is scalar and vector quantity with 20+ examples? Comparison, Types of vectors and more.
What is scalar and vector quantity
In physics, we come across various physical quantities such as distance, mass, velocity, speed, acceleration, momentum, electric current, electric flux, electric field, dipole moment, time, temperature, speed of light and so many.
These physical quantity divided into two main classes:
- Scalar quantities or Scalars
- Vector quantities or Vectors
In this article, we discuss all about of scalar and vector quantities. This is useful for all competitive exams, Entrance, TGT PGT (Physics), vectors class 11, vectors class 12. Please read carefully complete article.
What is Scalar Quantity | Scalars
What are Scalar Quantities ?
Those physical quantities which are pass only magnitude
or
Those physical quantities which are completely Defined by only magnitude no required direction in the space, called Scalar quantities.
List of Examples of Scalar quantities
- Mass, distance, time, volume
- temperature, pressure, heat, specific heat
- , speed, Speed of light
- electric current, electric flux, magnetic flux, electric potential
- Work, Energy, power
- Frequency
What are vectors in physics | Vectors
Vector quantity : Those physical quantities which possess both magnitude and direction and also obey vector algebraic rules.
or
Those physical quantities which can be completely defined by magnitude and direction are called vector quantities.
List of Examples of vector quantities
- Weight, Position, displacement, velocity, acceleration
- force, torque, impulse, momentum, thrust
- electric field, magnetic field, gravitational field
- electric current density
- amplitude, wavelength
- Area, surface area etc.
Special Note: A quantity having magnitude and direction is not necessarily a vector. For example, time and electric current. These quantities have magnitude and direction but they are scalar. This is because they do not obey the laws of vector addition.
Vector representation | Expression Of vector |How to write vectors?
We know that vectors have both magnitude and direction, so for the Expression of vector use an arrow overhead on the quantity.
\vec{A}=\mid\vec{A}\mid\hat{A}\Rightarrow or \Rightarrow\vec{A}=A\hat{A}
Where,
\vec{A}=vector A
|\vec{A}|=A =magnitude..of..vector A(or\vec{A})
and Â = direction of vector A
What is Tensor Quantity
A physical quantity which has different values in different directions is called a Tensor.
What are the Examples of Tensor:
- Moment of inertia
- refractive index
- stress, strain
- density
50 Examples of scalar and vector quantities
Distinguish between Scalar and Vector quantity
Difference between scalar and vector quantity| scalar vs vector| 20 examples of scalar and vector quantities
Scalars vs Vectors
Types of vectors
Depending on the nature of magnitude and direction, several types of vectors
What is Zero vectors | Null vector| Improper vector
Vectors having, Zero magnitudes and Arbitrary (unknown) directions, are called zero vectors.
Notation of zero vector
\overrightarrow{0}
What are the Properties of Null vectors
\overrightarrow{A}+\overrightarrow{0}=\overrightarrow{A}
\overrightarrow{A}×\overrightarrow{0}=\overrightarrow{0}
λ\overrightarrow{0}=\overrightarrow{0}
\overrightarrow{A}=\overrightarrow{B}\Rightarrow\overrightarrow{A}-\overrightarrow{B}=\overrightarrow{0}
If vector A and vector B are parallel to each other then
\overrightarrow{A}×\overrightarrow{B}=\overrightarrow{0}
What are the examples of null vectors:
- The position vector of a particle at the origin
- The displacement vector of a stationary object
- The acceleration vector of a particle moving with uniform velocity
What are unit vectors? Unit vectors
Vectors having unit magnitude and definite (known) direction, are called unit vectors.
We know that
\overrightarrow{A}=|\overrightarrow{A}|.Â
so that unit vector
Â=\frac{\overrightarrow{A}}{|\overrightarrow{A}|}
Properties of unit vector :
- Unit vectors gives only direction of vectors i.e. it indicates only direction.
- Unit vectors have no any unit.
What are Equal vectors
Two vectors are said to be equal when they have equal magnitudes and the same directions and represent the same physical quantity.
vector A and vector B be equal i.e.
\overrightarrow{A}=\overrightarrow{B}
when magnitude
|\overrightarrow{A}|=|\overrightarrow{B}|
and direction
\widehat{A}=\widehat{B}
What are Parallel vectors
Two Vectors A and B be parallel, i.e.
\overrightarrow{A}\parallel\overrightarrow{B}
when
1. Both have the same direction
\widehat{A}=\widehat{B}
2. One vector is scalar (+ve) non-zero multiple of another vector
\overrightarrow{A}=k\overrightarrow{B}
where k is any scalar or number.
What are Antiparallel vectors
Two vectors are said to be anti-parallel, when
1. Both have opposite direction
\widehat{A}=-\widehat{B}
2. One vector is a scalar non-zero (-ve) multiple of another vector.
\overrightarrow{A}=-k\overrightarrow{B}
where k is scalar or any number.
What are Collinear vectors
Those vectors, which act along the same line, are called collinear vectors. So the angle between them can be 0° or 180°.
Properties of Collinear vectors :
- Every colinear vectors becomes parallel vectors when angle between them be zero but consverse is not true.
- Every colinear vectors becomes antiparallel vectors when angle between them be 180° but converse is not true.
What is Polar vector quantity | Radial vectors
Vectors which directly point towards the direction of the vector quantity are called polar vectors.
Examples: Displacement, force, velocity, linear momentum, etc.
What are Axial vectors | Pseudo vectors
These represent rotational effects and are always along the axis of rotation in accordance with the right-handed screw rule.
Examples: Angular velocity, angular momentum, angular acceleration, Torque, etc.
what are coplanar vectors
Coplanar vectors : If three or more vectors lie in the same plane, then these are called coplanar vectors.
What are Negative Vectors
A vector of the same magnitude with the opposite direction of the given vector is called the negative vector of that vector.
If\mid\vec{A}\mid=\mid\vec{B}\mid with .. \hat{A}=-\hat{B}
then vectors A & B are said to be negative vectors of each vector.
What are Orthogonal vectors:
When three unit vectors (î, ĵ & k) are formed a right-handed triad then they are called orthogonal unit vectors.
What are Like and Unlike vectors
If the vector representing of a physical quantity has the same direction then they are called, Like vectors.
If they are oppositely directed they are called, Unlike vectors.
What are Concurrent vectors | Coinitial vectors
Vectors have the same origin, called Concurrent vectors or Coinitial vectors.
What are Gradient vectors
A gradient vector is a vector used to represent a vector field. Example: Electric intensity vector.
Addition and Subtraction of two vectors
Addition of two vectors
How to add vectors? If the angle between two non zero vectors A & B is θ then
- Magnitude of the resultant vectors(R)
- Direction of the resultant vectors
tan\beta=\frac{CD}{ON}=\frac{Asin\theta}{A+Bcos\theta}
Special Cases :
- R_{max} = A + B when θ = 0^{0}
- R_{min} = A – B when θ = 180^{0}
- R =√ (A^{2} + B^{2}) when θ = 90^{0}
Subtraction of two vectors
Direction of resultant vector
tan\alpha2=\frac{Bsin\theta}{A-Bcos\theta}
For complete study♡ of Addition and Subtraction of vectors click here
Multiplication of vectors|Product of two vectors
There are two types of multiplication/product of two vectors_
- Scalar product or Dot Product
- Vector Product or Cross Product
1.Dot product of two vectors | The scalar product of two vectors | Direct product of vectors
The dot product of two vectors is defined as the product of the magnitude of two vectors with the cosine of the angle between them.
\overrightarrow{A}.\overrightarrow{B}=ABcos\theta
2. Vector Product | Cross Product of two Vectors | Outer Product
If two vectors A & B having angle θ between them then their cross product is written as
\vec{A}\times\vec{B}\Rightarrow read ...as...\vec{A}cross\vec{B}
\vec{A}\times\vec{B}=[\vec{A},\vec{B}]=ABsin\theta\hat{n}
For Complete study♡ of “Multiplication of vectors” click here
Tips & Tricks about Scalars and vectors
- Similarities between scalar and vector quantity : A quantity having magnitude and direction is not necessarily a vector. For example, time and electric current. These quantities have magnitude and direction but they are scalar. This is because they do not obey the laws of vector addition.
- A vector can have only two rectangular components in-plane and only three rectangular components in space.
- A vector can have any number, even infinite components. (minimum 2 components)
- The rectangular components cannot have magnitude greater than that of the vector itself.
- Distance covered is a scalar quantity.
- The displacement is a vector quantity.
- Scalars are added, subtracted or divided algebraically.
- Vectors are added and subtracted geometrically.
- Division of vectors is not allowed as directions cannot be divided.
- Unit vector gives the direction of vector.
- The magnitude of unit vector is 1.
- Unit vector has no unit.
- Minimum number of collinear vectors whose resultant can be zero is two.
- Minimum number of coplanar vectors whose resultant is zero is three.
- Minimum number of non-coplanar vectors whose resultant is zero is four.
FAQs : Scalar and Vector quantity
What is vector and scalar quantity in Physics?
Scalars: Those physical quantities which are completely Defined by only magnitude no required direction in the space, called Scalar quantities. Example: Mass, Time, Electric current, Frequency etc.
Vectors : Those physical quantities which can be completely defined by magnitude and direction are called vector quantities. Example : Weight, Displacement, Electric current density, Amplitude etc.
i.e. >> Vectors have both magnitude and direction but Scalars have only magnitude.
What are 20 Examples of Scalars?
- Mass, Volume, Distance, Speed
- Temperature, Pressure, Time
- Electric charge, Electric current, Electric flux
- Electric potential, Magnetic flux
- Work, Energy, Power, Heat,
- Frequency, Speed of light, etc.
What are 20 Examples of vector quantity?
- Position, displacement, velocity,
- Acceleration, Momentum, weight,
- Force, torque, impulse, thrust,
- Electric field, magnetic field, gravitational field,
- Electric current density, area,
- Amplitude, wavelength, surface area, etc
Why can't the vectors be added algebraically?
Magnitudes can be added algebraically while vector has both magnitude and direction. But direction can be added geometrically not by algebraically, So vector can not be added algebraically.
How are vector and scalar different?
The main difference between vector and scalar is that Vectors have both magnitude and direction while Scalars have only magnitude.
Is it possible to add any two vectors?
No. It is not possible to add any two vectors, but we can add only vectors representing the same physical quantity.
Electric current is a quantity?
Electric current is a scalar quantity. Because electric current not obey vector addition property. Electric current added algebraically (Kirchhoff’s 1st law : Σi = 0)
Is time a vector or scalar?
Scalar, like as electric current time does not obey vector addition rule so time is a scalar quantity.
speed is scalar or vector?
Speed is a scalar.
Is velocity a vector quantity?
yes, velocity is a vector quantity.
Momentum is scalar or vector?
momentum is a vector quantity.
what are unit vectors?
Vectors having unit magnitude and definite (known) direction, are called unit vectors.
Free Mock test: Introduction of Scalars and Vectors
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