PrepZii

table

Point Representation, Distance and Section Formula

The 3-Dimension chapter begins with points, distance from axes, section formula, and midpoint.

Topic	Formula
Position vector of $P(x,y,z)$	$x\hat i+y\hat j+z\hat k$
3D distance	$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$
Distance from coordinate axes	$PA=\sqrt{y^2+z^2}$ , $PB=\sqrt{z^2+x^2}$ , $PC=\sqrt{x^2+y^2}$
Section formula	$x=\frac{mx_2+nx_1}{m+n}$ , $y=\frac{my_2+ny_1}{m+n}$ , $z=\frac{mz_2+nz_1}{m+n}$
Midpoint	$x=\frac{x_1+x_2}{2}$ , $y=\frac{y_1+y_2}{2}$ , $z=\frac{z_1+z_2}{2}$

$x$

variable or coordinate