JEE Main 2020 (Online) 7th January Evening ShiftQuestion 1
If the foot of the perpendicular drawn from the point $(1,0,3)$ on a line passing through $(\alpha,7,1)$ is $\left(\frac53,\frac73,\frac{17}3\right)$, then $\alpha$ is equal to
3D Geometry
Answer$4$
Solution
$\overrightarrow{AF}=(\frac23,\frac73,\frac83)\parallel(2,7,8)$ must be perpendicular to the line direction $F-(\alpha,7,1)=(\frac53-\alpha,-\frac{14}3,\frac{14}3)$: $2(\frac53-\alpha)-\frac{98}3+\frac{112}3=0$, so $\alpha=4$.