MathsJEE Main 6 Apr 2026, Shift 1·Q15·MCQ·Tough

3D Geometry · Image of point in line

Let the image of the point

P(1, 6, a)

in the line

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

,

b > 0

, be

\left(\dfrac{a}{3}, 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:

(1)19
(2)20
(3)21
(4)22

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