Question 1: Define what is meant by scalars and vectors. Give five examples of each. Also with the help of examples explain the graphical representation of a vector.

Answer

Both scalars and vectors are physical quantities. The main difference between them is vectors are directional quantities whereas scalars need not any mention of direction. They are defined as;

Scalars

Scalars are those physical quantities which can be completely specified by its magnitude. (Magnitude may be imagined as size of the quantity).

So, for a complete description of scalar quantities, both number and unit are essential. The number and unit are called magnitude. Mass of 2 kilograms, time of 5 seconds and volume of 3 m³ are examples. Here 2, 5 and 3 are numbers and kilogram, second and m³ are the respective units.

Algebra of scalars is the same as the algebra of real numbers, that is, scalars can be added, multiplied, subtracted and divided by the usual arithmetical methods.

Examples of scalars

Mass, density, volume, temperature and speed are five examples of scalar quantities.

Some quantities refer to time; for example one year, month or second. Don’t confuse them whether they are vector or scalar quantities. All such quantities that refer to time are scalar.

Vectors

Vectors are those physical quantities which can be specified by its magnitude as well as direction.

So, to describe a vector completely we must mention its magnitude (the numerical value and proper unit) along with a proper direction.

Vectors have their own algebra of addition, subtraction and multiplication. However, division of one vector on other is not possible.

Examples of vectors

Displacement, force, momentum, torque and velocity are five examples of vectors.

فرض کریں ایک آدمی ایک قدم تیزی سے آگے کی طرف لیتا ہے اور دوسرے ہی لمحے میں دوسرا قدم پیچھے کی طرف۔ کیا اس کی رفتار ایک ویکٹر کوانٹیٹی ہے؟ (نہیں)۔