Find the coordinates of the foot of perpendicular drawn from origin to the planes: `2x-3y+4z-6=0`

Explanation

The direction ratio of `{OP}` are proportional to `2,-3,4`


So, cartesian equation of OP are `\frac{x}{2}=\frac{y}{-3}=\frac{z}{4}`


The coordinates of `P` are given by `\frac{x}{2}=\frac{y}{-3}=\frac{z}{4}=r`


The coordinates of `{P}` are `(2 r-3 r, 4 r)`.


It lies on `2 x-3 y+4 z-6=0`


`\therefore 4{r}+9{r}+16{r}-6=0 \Rightarrow {r}=\frac{6}{29}`


Therefore, the coordinates of `P` are `(\frac{12}{29}, \frac{-18}{29}, \frac{24}{29})`