Vectors-Types And Components
VECTORS - TYPES & COMPONENTS
All measurable quantities are called physical quantities.
Physical quantities are classified into scalars and vectors.
Scalar Quantities: Physical quantities having only magnitude are called scalars.
Examples: Length, area, volume, distance, speed, mass, time, temperature, density, work, energy, power etc. are scalars.
Vector Quantities: Physical quantities having both magnitude and direction and which obey the laws of vector addition are called vectors.
Vectors are represented with letters with an arrow above it () or with a letter a bar above it () or just with a bold letter (a)
Examples : Displacement, velocity, acceleration, momentum, force, impulse, torque etc. are vectors
To describe a vector quantity we require
a) The specific unit of that quantity.
b) The number of times that unit is contained in that quantity (magnitude).
c) the orientation of that quantity.
Example: A bird is flying from east to west with a velocity of 100ms-1.
Note: A physical quantity having magnitude and direction but not obeying laws of vector addition is treated as a scalar.
For example, A current in a wire is represented by the direction but it is not vector quantity because it does not obey the laws of vector addition.
Geometrical Representation of vector and its magnitude: A vector is represented by a directed line segment. Length of that line segment is proportional to the magnitude of the physical quantity which it represents and the arrow of that denotes the direction of vector.
For example if a displacement of 1 meter is represented by a vector of length 1 unit, then a displacement of 2 meter is represented by a vector of length 2 units.
Cartesian co–ordinate system: In order to describe the motion of an object we must specify its position relative to observer. One of the most convenient co – ordinate system is Cartesian co–ordinate system. It consists of three mutually perpendicular axes designated as x – axis, y–axis and z–axis. Location of any point p is specified by three co–ordinates x, y, and z as shown in the figure.