Question

Find the distance of a point $3x-4y+122=3$ from the origin.

Answer 1

The distance from a point $P(0,0,0)$ from the given plane $3x-4y+12z-3=0$ is:

$D=\frac{|3\times 0-4\times 0+12\times 0-3|}{\sqrt{{\left(3\right)}^2+{(-4)}^2+{\left(12\right)}^2}}$

$=\frac{3}{\sqrt{9+16+144}}$

$=\frac{3}{\sqrt{169}}$

$=\frac{3}{13}$ units.