The coordinates of the foot of perpendicular from the point (1,0,0) to the line x-12=y+1-3…

Question

The coordinates of the foot of perpendicular from the point $(1,0,0)$ to the line $\dfrac{x-1}2=\dfrac{y+1}{-3}=\dfrac{z+10}8$ are

Accepted Answer

$A=(1,-1,-10)$, direction $(2,-3,8)$. $\overrightarrow{AP}=(0,1,10)$ where $P=(1,0,0)$.
$$k=\frac{\overrightarrow{AP}\cdot(2,-3,8)}{4+9+64}=\frac{0-3+80}{77}=1.$$
Foot $=A+k(2,-3,8)=(3,-4,-2)$.

Solutions · 1