8.0 Cartesian co-ordinate system

  Basic Vectors

A cartesian coordinate system is defined by $3$ axes that are mutually perpendicular to each other. These $3$ axes are abbreviated as $x$, $y$ and $z$ axis.

The position of any point in cartesian space can be defined wrt to these axes.

Point where $x$, $y$ and $z$ axes intersect is known as origin and its coordinate is $\left( {0,0,0} \right)$.

If any point is having a coordinate $\left( {a,b,c} \right)$ as shown in the figure.

Then,

$a$ is the distance along $x$ axis from origin $O$
$b$ is the distance along $y$ axis from origin $O$
$c$ is the distance along $z$ axis from origin $O$

Now the distance between origin and point $P$ is given by,

$$OP = \sqrt {{{\left( {a - 0} \right)}^2} + {{\left( {b - 0} \right)}^2} + {{\left( {c - 0} \right)}^2}} $$$$OP = \sqrt {{a^2} + {b^2} + {c^2}} $$