Mention four importance of writing the physical quantities as vectors.

Explanation:

Knowledge of vectors is important because many quantities used in physics are vectors. If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect.

Some of the key vector quantities in physics: force, displacement, velocity, and acceleration.

An example of the importance of vector addition could be the following:

Two cars are involved in a collision. At the time of the collision car A was travelling at 40 mph, car B was travelling at 60 mph. Until I tell you in which directions the cars were travelling you don't know how serious the collision was.

The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of 100 mph!

physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as the combination of a numerical value and a unit. For example, the physical quantity mass can be quantified as n kg, where n is the numerical value and kg is the unit.A physical quantity possesses at least two characteristics in common, one is numerical magnitude and other is the unit in which it is measured.

Symbols and nomenclatureEdit

International recommendations for the use of symbols for quantities are set out in ISO/IEC 80000, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity mass is m, and the recommended symbol for the quantity electric charge is Q.

Subscripts and indicesEdit

Subscripts are used for two reasons, to simply attach a name to the quantity or associate it with another quantity, or represent a specific vector, matrix, or tensor component.[clarification needed]

Name reference: The quantity has a subscripted or superscripted single letter, group of letters, or complete word, to label what concept or entity they refer to, often to distinguish it from other quanities with the same main symbol. These subscripts or superscripts tend to be written in upright roman typeface rather than italic while the main symbol representing the quantity is in italic. For instance Ek or Ekinetic is usually used to denote kinetic energy and Ep or Epotential is usually used to denote potential energy.

Quantity reference: The quantity has a subscripted or superscripted single letter, group of letters, or complete word, to parameterize what measurement/s they refer to. These subscripts or superscripts tend to be written in italic rather than upright roman typeface; the main symbol representing the quantity is in italic. For example cp or cpressure is heat capacity at the pressure given by the quantity in the subscript.

The type of subscript is expressed by its typeface: 'k' and 'p' are abbreviations of the words kinetic and potential, whereas p (italic) is the symbol for the physical quantity pressure rather than an abbreviation of the word.

Indices: The use of indices is for mathematical formalism using index notation.

ScalarsEdit

A scalar is a physical quantity that has magnitude but no direction. Symbols for physical quantities are usually chosen to be a single letter of the Latin or Greek alphabet, and are printed in italic type.

VectorsEdit

Vectors are physical quantities that possess both magnitude and direction. Symbols for physical quantities that are vectors are in bold type, underlined or with an arrow above. For example, if u is the speed of a particle, then the straightforward notations for its velocity are u, u, or {\displaystyle {\vec {u}}\,\!}\vec{u}\,\!.

Numbers and elementary functionsEdit

Numerical quantities, even those denoted by letters, are usually printed in roman (upright) type, though sometimes in italic. Symbols for elementary functions (circular trigonometric, hyperbolic, logarithmic etc.), changes in a quantity like Δ in Δy or operators like d in dx, are also recommended to be printed in roman type.

Examples:

Real numbers, such as 1 or √2,

e, the base of natural logarithms,

i, the imaginary unit,

π for the ratio of a circle's circumference to its diameter, 3.14159265358979323846264338327950288...

δx, Δy, dz, representing differences (finite or otherwise) in the quantities x, y and z

sin α, sinh γ, log x

chemical properties of thing

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day