What is Physical Quantities?Quantities which can be
observed as well as measured are called physical quantities. OR Quantities in terms of
which all the laws of physics can be expressed are called physical
quantities.  Types of Physical quantities.There are two types of Physical Quantities.
What is Scalar Quantity?A physical quantity
which has magnitude only is called scalar quantity. Examples: Time, distance, mass,
temperature, speed, energy, work, volume, area, electric charge etc. What is Vector Quantity?A physical quantity which has both magnitude and direction is
called vector quantity. Examples: Force, velocity, displacement, torque, momentum, acceleration, weight, angular velocity, electric intensity etc. |
How is a vector represented?A vector is represented
in two ways.
What is symbolic Representation?It is represented by bold face letter such as A, d, r and v etc.
It can be also be represented by a letter with an arrow placed above or below
the letter such as A or A. What is Graphical Representation?It is represented by a straight line with an arrow head at its
one end. The length of line represents magnitude of vector (according to
suitable scale). Arrow head represents the direction of vector. Note: Representation
of magnitude of vector
The magnitude of vector is represented by light face letter such as A, d, rand v etc, or by the modulus of a vector such as etc. |
What is rectangular
coordinate system? || (Cartesian Co-ordinate System) ?
The set of two or three mutually perpendicular lines
intersecting at a point is called rectangular coordinate
system or Cartesian Co-ordinate System . The lines are called coordinate axes. One of
these lines is called x-axis (or horizontal axis) The
other is called y- axis or vertical axis. The line
perpendicular to both x and y -axes is called z-axis. The point of
intersection is called origin. Two dimensional
coordinate system (Plane)
If the system consists of two perpendicular lines then it is
called two dimensional coordinate system. Direction of a vector in planeIt is represented by the angle which the vector makes with
positive x- axis in anti-clock wise direction.  Three dimensional
co-ordinate systems (Space)
If the system consists of three perpendicular lines, then it is
called three dimensional co-ordinate systems. Direction of a vector in spaceIt is represented by three angles which the vector makes with x, y and z-axes.  |
Describe the addition of vectors by head to tail rule.What is Head to tail rule?It is a graphical method to add two or more vectors. Explanation: Draw the representative lines of vectors vector A and vector B Join the tail of vector vector B , with the head of vector vector A Join the tail of vector vector A with head of vector vector B.  This Line given the magnitude of resultant vactor R . The direction of resultant vector is from tail of vector A to the head of vector B. What is Commutative Property?From figure, it is clear that either we add vector A to vector B or vector B to vector A , the resultant is same. ie, vector A + vector B = vector B + vector A It means that when vectors are added, the result is the same for any order of addition. Hence vector addition is commutative.  |
What is Resultant Vector?A vector which has the same effect as the combined effect of all the vectors to be added is called resultant vector. What is Vectors Subtraction?The subtraction of a vector is equivalent to the addition of same vector with its direction reversed.  Explanation: Consider two vectors vector A and vector B To subtract vector B from vector vector A First, take the negative of vector vector B Add (- vector B ) into vector vector A graphically as shown in fig. So vector A * vector B = vector A +(- vector B ). |
Explain Multiplication of a vector by a scalar?A vector can be multiplied by
 Explain Vector Multiplication with positive number?When a vector vec A is multiplied by a positive number n (ie. n > 0 ) Then the product vector will have magnitude equal to nA and same direction as that of vector A. Explain Multiplication with negative number?When a vector vector A is multiplied by a negative number n (i.e. n < 0 , then the product magnitude equal to nA but direction opposite to that of vector A. Explain Multiplication with scalar quantity?When a vector vector A is multiplied by a scalar quantity n, then the product vector will be whose dimensions are equal to the product of dimensions of n and vector A. Examples: ➤ Product of mass m and velocity vector v is momentum[ vector P =m vector v ➤ Product of mass m and acceleration vector a is force vector F =m vector a ] ➤ Product of force vector F time impulse \ vector 1 = vector Ft \ |
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What is Null or Zero Vector?A vector whose magnitude is zero and direction arbitrary is called a null vector. It is represented by vector O.  Example: ➤ Sum of a vector vec A and its negative vector (- vector A ) is a null vector. i.e. vector A +(- vector A )= vector 0 ➤ Sum of vectors taken head to tail along the sides of a closed polygon is null vector. |
What is Equal Vectors?The vectors are said to be equal vectors if they have same magnitude and same direction regardless of the position of their initial points.  Example: Two parallel vector vector A and vector B of same magnitude and direction are equal vectors. This line gives the magnitude of resultant vector vector R. The direction of resultant vector is from tail of vector vector A to the head of vector vector B. |
