JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Three Dimensional Geometry

Let the point, on the line passing through

P (1, - 2, 3)

and

Q (5, - 4, 7)

, farther from the origin and at a distance of 9 units from the point

P

, be

(α, β, γ)

. Then

α^{2} + β^{2} + γ^{2}

is equal to

(A)165
(B)150
(C)155✓ Correct
(D)160

Answer: (C)

Solution

Direction of

P Q

Q - P = (4, - 2, 4) ∥ (2, - 1, 2)

, magnitude 3, unit vector

\frac{1}{3} (2, - 1, 2)

.

The point at distance 9 from

P (1, - 2, 3)

farther from the origin is

P + 9 \cdot \frac{1}{3} (2, - 1, 2) = (1, - 2, 3) + (6, - 3, 6) = (7, - 5, 9) .

α^{2} + β^{2} + γ^{2} = 49 + 25 + 81 = 155.

Option C.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Single correct option

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