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...