Download scalars and vectors

BY: ATUL SORAL
IBDP EDUCATOR PHYSICS
SCALARS
Those physical quantities which
possess only magnitude and no
direction is required are called
scalars.
Eg.
Mass,
length,
distance,
temperature, all real numbers, etc.
VECTORS
Those physical quantities which possess
both magnitude and direction are
called vector quantities.
Eg. Displacement, velocity, momentum,
force, acceleration, etc.
TENSORS (not in course)
Those physical quantities which have no specified
direction and have different values in different
directions are called tensors.
Eg. Moment of inertia.
Certain other physical quantities like density, stress,
strain, refractive index, dielectric constant, electrical
conductivity etc are scalars in isotropic media, But
these quantities assume different values in different
directions in anisotropic media and hence become
tensors.
REPRESENTATION OF A
VECTOR
A vector is represented on paper by an arrow
1. the length represents magnitude
2. the arrow faces the direction of motion
3. a vector can be “picked up” and moved on
the paper as long as the length and direction
its pointing does not change
TYPE OF VECTORs
(i) Fixed or Localized vector: If the initial point of a
vector is fixed, it is called a fixed vector.
(ii) Free or Non-localized vector: If the initial point of a
vector is not fixed, it is called a free vector.
(iii) Unit vector: the vector whose magnitude is unit and
direction is the same as that of the given vector. Is is
represented by  (A cap)
(iv) Equal vector: Two vectors are said to be equal if their
magnitude as well as directions are same.
(v) Negative vector: Vector is said to be negative if its
magnitude is same but direction is opposite to other.
TYPE OF VECTORs
(vi) Co initial vector: Two vectors if they have same initial
point then they are said to be co-initial vectors.
(vii) Collinear vector: Two vectors which either act along the
same line or along parallel lines, are called collinear
vectors.
(viii) Coplanar vectors: Vectors lying on the same plane are
called coplanar vector.
(ix) Zero vector: a vector whose magnitude is zero, is called
zero vector. Represented by ‘0’ with a cap
(x) Scalar multiplication of a vector: when a vector is
multiplied by any real number, the magnitude is raised by
that factor, but direction remains same.
TRIANGLE LAW OF VECTOR
ADDITION
Triangle law of vector addition states that when
two vectors are represented by two sides of
a triangle in magnitude and direction taken in same
order then third side of the third side of
that triangle represents in magnitude and direction
the resultant of the vectors.
PARALLELOGRAM LAW OF
VECTOR ADDITION
If two vector quantities are represented by two
adjacent sides or a parallelogram
then the diagonal of parallelogram will be equal
to the resultant of these two vectors.
POLYGON LAW OF VECTOR
ADDITION
If a number of vectors can be represented both in
magnitude and direction by the sides of an open
convex polygon taken in the same order, then the
resultant is represented completely in magnitude and
direction by the closing side of the polygon, taken in
the opposite order.
MAGNITUDE OF RESULTANT IN
VECTOR
PROPERTIES OF VECTOR
ADDITION
Addition is commutative: A + B = B + A
2. Addition is associative: A + (B + C ) = (A + B) + C
3. Addition is distributive: A (B + C ) = AB + AC
1.
SUBTRACTION OF VECTORS
 It is addition of negative vectors.
A – B = A + (-B)
RESOLUTION OF VECTORS
The process of splitting a vector in to component vectors
is called resolution.
The process of splitting a vector into components at right
angles to each other is called rectangular resolution of
a vector and the components are called its rectangular
components.
RESOLUTION OF VECTORS
WORK
 To find the examples for vector resolution in daily life.
 Students to work in home for individual research for
atleast 5 examples of vector resolution in daily life and
to explain the same in own words.