Vectors
Vectors Class 11 & 12 Notes
Physical Quantities: In physical science the quantities we can measure are called physical quantities.
Types of physical quantities
Physical quantities are categorized into two types. They are -
i) Fundamental quantities and
ii) Derived quantities.
Fundamental quantities: The quantities which do not depend on other quantities are called fundamental quantities. For example: mass, length, time, temperature, electric current, luminous intensity and amount of substance.
Derived quantities: The quantities which depend on two or more fundamental quantities are called derived quantities. For example: Area, Volume, Density, Speed, Velocity, Acceleration, Force, Work, Energy, etc.
According to representation types of physical quantities
According to representation physical quantities are two types. They are -
i) Scalar quantity and
ii) Vector quantity.
i) Scalar quantity: The physical quantities which can be represented only by magnitude are called scalar quantities. For example: mass, length, speed, work, time, temperature, etc.
ii) Vector quantity: The physical quantities whose representation needs both magnitude and direction are called vector quantities. For example: weight, displacement, velocity, force, electric intensity, etc. are vector quantities.
Properties of Vector
- Vectors have both magnitude and direction.
- Vectors can be changed by changing either magnitude or direction.
- Addition, subtraction or multiplication does not follow usual mathematical step.
- Vector multiplication depends on the angle between two vectors. The multiplication of two vectors can be zero but neither of the vectors can be zero.
Sign of Vectors: The representation of vectors necessitate direction. Any vector can be representation with a letter and (a) straight line segment.
With a letter: Vectors can be represented with letters in the following four ways:
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Difference between vector and scalar quantity
Sample
| No. | Vector Quantity | Scalar Quantity |
| 1 | The physical quantity which necessitate both magnitude and direction is called vector quantity. For example, displacement, velocity, weight and force are vector quantities. | The physical quantity which can be represented only with magnitude is called scalar quantity. For example, length, speed, mass and time are scalar quantities. |
| 2 | A vector quantity gets changed if either its magnitude or direction or both are changed. | Scalar quantity gets changed if only its magnitude is changed. |
| 3 | Addition, subtraction, multiplication of a vector quantity cannot be done by using usual algebraic rules. | Addition, subtraction and multiplication of a scalar quantity can be done by using usual algebraic rule. |
| 4 | Product of two vector quantities may be zero if any of the quantities is not zero. | Product of two scalar quantities can never be zero if any of the two quantities is not zero. |
| 5 | Special symbol is needed to represent a vector quantity. | No special symbol is needed to represent a scalar quantity. |
| 6 | Product of two vectors may be a scalar or a vector quantity depending on the way of multiplication. | Product of two scalar quantities always a scalar quantity. |
Expression of a Vector
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