## Chapter 11

## Three Dimension

##### 11.1 RECTANGULAR COORDiNATE AXES

To locate a point in a plane, two numbers are necessary. We know that any point in the *xy* plane can be represented as an ordered pair (*a*, *b*) of real numbers where *a* is called *x*-coordinate of the point and *b* is called the *y*-coordinate of the point. For this reason, a plane is called two dimensional.

To locate a point in space, three numbers are required. Any point in space is represented by an ordered triple (*a*,* **b*,* c*) of real numbers. To represent a point in space we first choose a fixed point ‘*O*’ (called the origin) and then three directed lines through *O* which are perpendicular to each other (called coordinate axes) and labelled *x*-axis, *y*-axis as being horizontal and *z*-axis as vertical ...