Vectors

Vectors Class 11 & 12 Notes

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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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*

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Difference between vector and scalar quantity