JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 1
If the image of the point $P(1,0,3)$ in the line joining the points $A(4,7,1)$ and $B(3,5,3)$ is $Q(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to :
3D Geometry
Solution
Line: $(4-t,7-2t,1+2t)$. $\vec{FP}\cdot(-1,-2,2)=9t-21=0$, $t=\frac73$, foot $F=(\frac53,\frac73,\frac{17}3)$. Image $Q=2F-P=(\frac73,\frac{14}3,\frac{25}3)$, sum $=\frac{46}3$.