JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Three Dimensional Geometry

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:

(A)11
(B)9
(C)6✓ Correct
(D)4

Answer: (C)

Solution

The line has direction

(1, 1, 2)

through

(0, 1, 2)

; the foot of the perpendicular from

P (1, 2, 7)

(λ, 1 + λ, 2 + 2 λ)

with

(1 - λ) + (1 - λ) + 2 (5 - 2 λ) = 0

, giving

λ = 2

and foot

(2, 3, 6)

. The image is

Q = 2 (2, 3, 6) - (1, 2, 7) = (3, 4, 5)

. The distance from

(a, 2, 5)

Q

(a - 3)^{2} + 4 = 4

, so

(a - 3)^{2} = 12

and

a = 3 \pm 23

. The sum of all possible values of

a

6

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Single correct option

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