JEE Main 2020 (Online) 5th September Morning ShiftQuestion 1
If $(a,b,c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}2=\frac{y-3}{-2}=\frac z{-1}$, then $a+b+c$ is equal to :
3D Geometry
Solution
Line through $A(-1,3,0)$, $d=(2,-2,-1)$. $F=A+ud$ with $(P-F)\cdot d=0$: $P-A=(2,-1,-3)$, $(P-A)\cdot d=4+2+3=9$, $d\cdot d=9\Rightarrow u=1$, $F=(1,1,-1)$. Image $=2F-P=(1,0,1)$, so $a+b+c=2$. Answer (C).