The foot of the perpendicular from 2,−4,0to the join of 0,0,0 , 0,3,0 is

Equation of the line joining $(0, 0, 0), (0, 3, 0)$ is $\frac{x}{0} = \frac{y}{3} = \frac{z}{0}$

General point on the above line is $Q (0, 3 y_{1}, 0)$

The direction ratios of the line joining $P (2, - 4, 0)$ and $Q (0, 3 y_{1}, 0)$ is $〈- 2, 3 y_{1} + 4, 0〉$

Since the line $P Q$ and $\frac{x}{0} = \frac{y}{3} = \frac{z}{0}$ are perpendicular to each other.

$\begin{matrix} 3 (3 y_{1} + 4) = 0 \\ y_{1} = - \frac{4}{3} \end{matrix}$

Therefore, the foot of the perpendicular of $(2, - 4, 0)$ to the join of $(0, 0, 0), (0, 3, 0)$ is $Q (0, - 4, 0)$

The foot of the perpendicular from $(2, - 4, 0)$ to the join of $(0, 0, 0), (0, 3, 0)$ is