Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 13 Introduction To Three-Dimensional Geometry will enable students to study smartly.

## CHSE Odisha 11th Class Math Notes Chapter 13 Introduction To Three-Dimensional Geometry

**Coordinates Of A Point In Space:**

In three-dimensional geometry three mutually perpendicular planes divide the space into eight equal parts. Each equal part is an octant.

(i) Sign of coordinate of a point in various octants.

(ii) Location of a point at 3D

Note:

(1) Coordinate of a point on x-axis is (x, 0, 0).

(2) Coordinate of a point on y-axis is (y, 0, 0).

(3) Coordinate of a point on z-axis is (y, 0, 0).

(4) Distance of a point (a, b, c) from x-axis = \(\sqrt{\mathrm{b}^2+\mathrm{c}^2}\)

(5) Distance of a point (a, b, c) from y-axis = \(\sqrt{\mathrm{a}^2+\mathrm{c}^2}\)

(6) Distance of a point (a, b, c) from z-axis = \(\sqrt{\mathrm{a}^2+\mathrm{b}^2}\)

Distance formula:

Distance between two points A(x_{1}, y_{1}, z_{1}) and B(x_{2}, y_{2}, z_{2}) = \(\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2+\left(\mathrm{z}_2-\mathrm{z}_1\right)^2}\)

**Division Formula (Section Formula):**

(i) Internal division:

If R(x, y, z) divides the join of A(x_{1}, y_{1}, z_{1}) and B(x_{2}, y_{2}, z_{2}) in ratio m: n internally then

\(\mathrm{x}=\frac{\mathrm{mx} \mathrm{x}_2+\mathrm{nx} \mathrm{x}_1}{\mathrm{~m}+\mathrm{n}}, \mathrm{y}=\frac{\mathrm{my} \mathrm{y}_2+\mathrm{ny} \mathrm{y}_1}{\mathrm{~m}+\mathrm{n}}\), \(\mathrm{z}=\frac{\mathrm{mz} \mathrm{z}_2+\mathrm{nz} \mathrm{z}_1}{\mathrm{~m}+\mathrm{n}}\)

(ii) External division:

If R divides AB in ratio m: n externally then \(x=\frac{m x_2-n x_1}{m-n}\), \(y=\frac{m y_2-n y_1}{m-n}, \frac{m z_2-n z_1}{m-n}\)

(iii) Midpoint formula:

If R is the midpoint of AB then