JEE Main · 2004 · 24 Apr 2004 · Offline · Three Dimensional Geometry

A line with direction cosines proportional to

2, 1, 2

meets each of the lines

x = y + a = z

and

x + a = 2 y = 2 z

. The co-ordinates of each of the point of intersection are given by

Answer: (B)

Solution

Parametrise the first line

x = y + a = z

(t, t - a, t)

and the second

x + a = 2 y = 2 z

(2 s - a, s, s)

. The transversal joining a point of one to a point of the other must point along

(2, 1, 2)

, so

(2 s - a - t, s - t + a, s - t) = κ (2, 1, 2)

. The last two components give

s - t + a = κ

and

s - t = 2 κ

, so

a = - κ

; the first gives

2 s - a - t = 2 κ

. Solving,

s = a

and

t = 3 a

, so the points are

(t, t - a, t) = (3 a, 2 a, 3 a)

and

(2 s - a, s, s) = (a, a, a)

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option