JEE Main · 2024 · 09 Apr 2024 · Shift 1 · Three Dimensional Geometry

The shortest distance between the line

\frac{x - 3}{4} = \frac{y + 7}{- 11} = \frac{z - 1}{5}

and

\frac{x - 5}{3} = \frac{y - 9}{- 6} = \frac{z + 2}{1}

is :

(A) $\frac{187}{563}$ ✓ Correct
(B) $\frac{178}{563}$
(C) $\frac{185}{563}$
(D) $\frac{179}{563}$

Answer: (A)

Solution

Direction of the common perpendicular:

n = (4, - 11, 5) \times (3, - 6, 1) = (19, 11, 9)

∣ n ∣ = 563

. With points

A (3, - 7, 1)

and

B (5, 9, - 2)

A B = (2, 16, - 3)

, so

d = \frac{∣ A B \cdot n ∣}{∣ n ∣} = \frac{∣38 + 176 - 27∣}{563} = \frac{187}{563}

— option (1).

JEE Main · 2024 · 09 Apr 2024 · Shift 1 · Single correct option

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