If the distance of the point (a,2,5) from the image of the point (1,2,7) in the line (x)/(1)=(y-1)/(1)=(z-2)/(2) is 4 , then the sum of all possible values of a is equal to :

3D Geometry: If the distance of the point (a,2,5) from the image of the point… | JEE Main 2026

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 1

If the distance of the point $(a,2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is $4$, then the sum of all possible values of $a$ is equal to :

3D Geometry

$11$$9$$6$✓ Correct answer$4$

Solution

Foot of $(1,2,7)$ on the line: $t=2$, $F=(2,3,6)$; image $(3,4,5)$. $(a-3)^2+4+0=16$ gives $a=3\pm2\sqrt3$, sum $=6$.

3D Geometry - JEE Mathematics question (JEE Main 2026 (Online) 5th April Evening Shift)

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