If the length of the perpendicular drawn from the point P(a, 4,2), a >0 on the line (x+1)/2=(y-3)/3=(z-1)/(-1) is 2 √(6) units and Q(α₁, α₂, α₃) is the image of the point P in this line, then a+Σ i=1 ³ α i is equal to:

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Evening shift · Q2507

JEE Main 202227 Jul, Evening shiftMathematicsHardThree Dimensional Geometry249× since 2002

If the length of the perpendicular drawn from the point

P(a, 4,2)

, a

>0

on the line

\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}

2 \sqrt{6}

units and

Q\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)

is the image of the point P in this line, then

\mathrm{a}+\sum\limits_{i=1}^{3} \alpha_{i}

is equal to :