Scalar and vector important Points:
All physical quantities having direction are not vectors. For
example, the electric current possesses direction but it is a scalar quantity because it can not be added or multiplied according to the rules
of vector algebra.
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)
Following quantities are neither vectors nor scalars :
Relative density, density, viscosity, frequency, pressure, stress, strain, modulus of elasticity, poisson’s ratio, moment of inertia, specific heat, latent heat, spring constant loudness, resistance, conductance, reactance, impedance,permittivity, dielectric constant, permeability, susceptibility, refractive index, focal length, power of lens, Boltzman constant, Stefan’s constant, Gas constant, Gravitational constant, Rydberg constant, Planck’s constant etc.
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.
Magnitude of unit vector is 1.
Minimum number of collinear vectors whose resultant can be zero
is two.
Minimum number of coplaner vectors whose resultant is zero is
three.
Minimum number of non coplaner vectors whose resultant is zero
is four.
Two vectors are perpendicular to each other if A.B 0
.
Two vectors are parallel to each other if A B 0.
Displacement, velocity, linear momentum and force are polar
vectors.
Angular velocity, angular acceleration, torque and angular
momentum are axial vectors.
Division with a vector is not defined because it is not possible to
divide with a direction.
Distance covered is always positive quantity.
The components of a vectors can have magnitude than that of the
vector itself.
The rectangular components cannot have magnitude greater than
that of the vector itself.
When we multiply a vector with 0 the product becomes a null
vector.
The resultant of two vectors of unequal magnitude can never be a
null vector.
Three vectors not lying in a plane can never add up to give a null
vector.
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 physical quantity which has different values in different
directions is called a tensor. For example : Moment of inertia has
different values in different directions. Hence moment of inertia is a
tensor. Other examples of tensor are refractive index, stress, strain,
density etc.
The magnitude of rectangular components of a vector is always less
than the magnitude of the vector
All physical quantities having direction are not vectors. For
example, the electric current possesses direction but it is a scalar quantity because it can not be added or multiplied according to the rules
of vector algebra.
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)
Following quantities are neither vectors nor scalars :
Relative density, density, viscosity, frequency, pressure, stress, strain, modulus of elasticity, poisson’s ratio, moment of inertia, specific heat, latent heat, spring constant loudness, resistance, conductance, reactance, impedance,permittivity, dielectric constant, permeability, susceptibility, refractive index, focal length, power of lens, Boltzman constant, Stefan’s constant, Gas constant, Gravitational constant, Rydberg constant, Planck’s constant etc.
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.
Magnitude of unit vector is 1.
Minimum number of collinear vectors whose resultant can be zero
is two.
Minimum number of coplaner vectors whose resultant is zero is
three.
Minimum number of non coplaner vectors whose resultant is zero
is four.
Two vectors are perpendicular to each other if A.B 0
.
Two vectors are parallel to each other if A B 0.
Displacement, velocity, linear momentum and force are polar
vectors.
Angular velocity, angular acceleration, torque and angular
momentum are axial vectors.
Division with a vector is not defined because it is not possible to
divide with a direction.
Distance covered is always positive quantity.
The components of a vectors can have magnitude than that of the
vector itself.
The rectangular components cannot have magnitude greater than
that of the vector itself.
When we multiply a vector with 0 the product becomes a null
vector.
The resultant of two vectors of unequal magnitude can never be a
null vector.
Three vectors not lying in a plane can never add up to give a null
vector.
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 physical quantity which has different values in different
directions is called a tensor. For example : Moment of inertia has
different values in different directions. Hence moment of inertia is a
tensor. Other examples of tensor are refractive index, stress, strain,
density etc.
The magnitude of rectangular components of a vector is always less
than the magnitude of the vector
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