Coordinate planes divide the space into octants.

(i) In three dimensions, the coordinate axes of a rectangular Cartesian coordinate system are three mutually perpendicular lines. The axes are called the $x,y$ and $z$ axes.

(ii) The three planes determined by the pair of axes are the coordinate planes. These planes are called $xy,yz$ and $zx$ planes and they divide the space into eight regions known as octants.

(iii) The coordinates of a point $P$ in the space are the perpendicular distances from $P$ on three mutually perpendicular coordinates planes $yz,zx$ and $xy$ respectively. The coordinates of a point $P$ are written in the form of triplet like $\left(x,y,z\right)$.

(iv) The coordinates of a point are also the distances from the origin of the feet of the perpendiculars from the point on the respective coordinate axes.

(v) The coordinates of any point on:

(a) $x-$axis are of the form $\left(x,0,0\right)$

(b) $y-$axis are of the form $\left(0,y,0\right)$

(c) $z-$axis are of the form $\left(0,0,z\right)$

(d) $xy-$plane are of the form $\left(x,y,0\right)$

(e) $yz-$plane are of the form $\left(0,y,z\right)$

(f) $zx-$plane are of the form $\left(x,0,z\right)$

2. Distance Formula

(i) The distance between two points $P\left(x_1,y_1, z_1\right)$ and $Q\left(x_2,y_2,z_2\right)$ is given by $PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2\mathrm{ }}$.

(ii) The distance of a point $P\left(x,y,z\right)$ from the origin $O\left(0,0,0\right)$ is given by $OP=\sqrt{x^2+y^2+z^2}$.

3. Section Formula:

The coordinates of the point $R$ which divides the line segment joining two points $P\left(x_1,y_1,z_1\right)$ and $Q\left(x_2,y_2,z_2\right)$ internally and externally in the ratio $m:n$ are given $\left(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n}\right)$ and $\left(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n},\frac{m{z}_2-n{z}_1}{m-n}\right)$ respectively.

4. Mid-Point Formula:

The coordinates of the mid-point of the line segment joining two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mathrm{ },\frac{z_1+z_2}{2}\right)$.

5. Centroid of Triangle:

The coordinates of the centroid of the triangle whose vertices are $\left(x_1,y_1,z_1\right),\left(x_2,y_2,z_2\right)$ and $\left(x_3,y_3,z_3\right)$ are $\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3}\right)$.