The coordinates of the foot of the perpendicular drawn from the origin to the line joining the points (-9, 4,5) and (10, 0, -1) will be

let AD be the perpendicular and D be the foot of the perpendicular which divides BC in the ratio $\lambda :1$ then
$D\left(\frac{10\lambda -9}{\lambda +1},\frac{4}{\lambda +1},\frac{-\lambda +5}{\lambda +1}\right)-----\left(1\right)$

$\text{ The direction ratios of }AD\text{ are }\frac{10\lambda -9}{\lambda +1},\frac{4}{\lambda +1}\text{ and }\frac{-\lambda +5}{\lambda +1}$

$\text{ and direction ratios of }BC\text{ are }19,-4\text{ and }-6\text{. }$

$\text{ Since }AD\perp BC\text{, we get }$

$19\left(\frac{10\lambda -9}{\lambda +1}\right)-4\left(\frac{4}{\lambda +1}\right)-6\left(\frac{-\lambda +5}{\lambda +1}\right)=0$

$\text{ or }\lambda =\frac{31}{28}$

$\text{ Hence, on putting the value of }\lambda \text{ in (i), we get required foot of }$

$\text{ the perpendicular, i.e., }\left(\frac{58}{59},\frac{112}{59},\frac{109}{59}\right)\text{. }$