# 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.
• 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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