Let the image of the point P(1,6,a) in the line L:x/1=(y-1)/2=(z-a+1)/b, b>0, be (a/3,0,a+c). If S(α,β,γ), α>0, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is 2√(14), then α+β+γ is equal to:

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 6 Apr, Morning shift · Q15

JEE Main 20266 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the image of the point

P(1,6,a)

in the line

L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}

b>0

, be

\left(\frac a3,0,a+c\right)

. If

S(\alpha,\beta,\gamma)

\alpha>0

, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is

2\sqrt{14}

, then

\alpha+\beta+\gamma

is equal to: