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02 - Vectors & Equilibrium

Vectors & Equilibrium

Vectors

A physical quantity which have both magnitude and direction is called a vector quantity.

Representation of Vectors

  • Symbolically, a vector can be represented by
    • An arrow head on top or bottom of a letter. like \(\overrightarrow{a}\), \(\underrightarrow{a}\)
    • A bar on top or bottom like \(\overline{a}\), \(\underline{a}\)
    • Bold face letters like a
  • Graphically, a vector can be represented by drawing a line and putting arrow head on it.

Rectangular Coordinate System

Two dimensional

  • It consists of two mutually perpendicular intersecting lines, called x-axis & y-axis
  • One angle is enough to specify the direction of a vector in two-dimensional coordinate system.

Three-dimensional

  • It consists of three mutually perpendicular lines called x-axis, y-axis & z-axis
  • The direction of a vector in three dimensional rectangular coordinate system is specified by three angles making x, y & z-axis.

Origin

  • It is the point where mutually perpendicular lines in rectangular coordinate system.
  • In 2d plane it is \((0,0)\)
  • In 3d space it is \((0,0,0)\)

Unit Vector

  • Unit vector has magnitude of 1.
  • It is represented by an hat on them like \(\hat{a}\).
  • It is used to represent direction of vector.

To be completed...

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